Publications : articles*

 [1] "Analyticity of Wightman functions at completely space-like points." Helv. Phys. Acta 32, 135-137(1959).
 [2] "Domain of holomorphy of the three-point function." Helv. Phys. Acta 34, 587-592(1961).
 [3] "Connection between Wightman functions and Green functions in p-space." Nuovo Cim. 19, 356-376(1961). (pdf)
 [4] (with K. Hepp, R. Jost and O. Steinmann) "Necessary restriction on Wightman functions." Helv. Phys. Acta 34, 542-544(1961).
 [5] "On the asymptotic condition in quantum field theory." Helv. Phys. Acta 35, 147-163(1962).
 [6] (with H. Araki and K. Hepp) "On the asymptotic behaviour of Wightman functions in space-like directions." Helv. Phys. Acta 35, 164-174(1962).
 [7] "Classical statistical mechanics of a system of particles." Helv. Phys. Acta 36, 183-197(1963).
 [8] "Statistical mechanics of quantum systems of particles." Helv. Phys. Acta 36, 789-799(1963).
 [9] "Correlation functions of classical gases." Ann. Phys. (N.Y.) 25, 109-120(1963).
 [10] "Cluster property of the correlation functions of classical gases." Rev. Mod. Phys. 36, 580-584(1964).
 [11] "Correlation functionals." J. Math. Phys. 6, 201-220(1965).
 [12] (with M.E. Fisher) "The stability of many-particle systems." J. Math. Phys. 7, 260-270(1966). (pdf)
 [13] (with G.-F. Dell'Antonio and S. Doplicher) "A theorem on canonical commutation and anticommutation relations." Commun. Math. Phys. 2, 223-230(1966). (pdf)
 [14] "States of physical systems." Commun. Math. Phys. 3, 133-150(1966). (pdf)
 [15] (with J. Ginibre and A. Grossmann) "Condensation of lattice gases." Commun. Math. Phys. 3, 187-193(1966). (pdf)
 [16] (with D.W. Robinson) "Extremal invariant states." Ann. Inst. Henri Poincaré 6, 299-310(1967).  (pdf)
 [17] (with D.W. Robinson) "Mean entropy of states in classical statistical mechanics." Commun. Math. Phys. 5, 288-300(1967). (pdf)
 [18] "A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule." Commun. Math. Phys. 5, 324-329(1967). (pdf)
 [19] (with O.E. Lanford) "Integral representation of invariant states on B*-algebras." J. Math. Phys. 8, 1460-1464(1967). (pdf)
 [20] "States of classical statistical mechanics." J. Math. Phys. 8, 1657-1668(1967). (pdf)
 [21] "Statistical mechanics of a one-dimensional lattice gas." Commun. Math. Phys. 9, 267-278(1968). (pdf)
 [22] (with G. Gallavotti and S. Miracle-Sole) "Absence of phase transitions in one-dimensional systems with hard cores." Physics Letters 26 A, 350-351(1968).
 [23] "Potentials of the Lennard-Jones type." Suppl. New Physics (Korean Phys. Soc.) 7 No 2, 50-55(1968).
 [24] "Some remarks on the ground state of infinite systems in statistical mechanics." Commun. Math. Phys. 11, 339-345(1969). (pdf)
 [25] "A remark on bound states in potential scattering theory." Nuovo Cim. 61 A, 655-662(1969). (pdf)
 [26] (with O.E. Lanford) "Observables at infinity and states with short range correlations in statistical mechanics." Commun. Math. Phys. 13, 194-215(1969). (pdf)
 [27] "Integral representation of states on a C*-algebra." J. Functional Analysis 6, 116-151(1970). (pdf)
 [28] "Superstable interactions in classical statistical mechanics." Commun. Math. Phys. 18, 127-159(1970). (pdf)
 [29] (with F. Takens) "On the nature of turbulence." Commun. Math. Phys. 20, 167-192(1971) and 23, 343-344(1971). (pdf)
 [30] "Analyticity of Green's functions of dilute quantum gases." J. Math. Phys. 12, 901-903(1971). (pdf)
 [31] "Extension of the Lee-Yang circle theorem." Phys. Rev. Letters 26, 303-304 (1971). (pdf)
 [32] (with R.B. Griffiths) "Strict convexity ("continuity") of the pressure in lattice systems." Commun. Math. Phys. 23, 169-175(1971). (pdf)
 [33] "Existence of a phase transition in a continuous classical system." Phys. Rev. Letters 27, 1040-1041(1971). (pdf)
 [34] "On the use of "small external fields" in the problem of symmetry breakdown in statistical mechanics." Ann. of Phys. 69, 364-374(1072). (pdf)
 [35] (with E.H. Lieb) "A property of zeros of the partition function for Ising spin systems." J. Math. Phys. 13, 781-784(1972).
 [36] "Definition of Green's functions for dilute Fermi gases." Helv. Phys. Acta 45, 215-219(1972).
 [37] "Statistical mechanics on a compact set with ${ Z^\nu$-action satisfying expansiveness and specification." Bull. Amer. Math. Soc. 78, 988-991(1972). (pdf)
 [38] "Statistical mechanics on a compact set with ${Z^\nu$-action satisfying expansiveness and specification." Trans. Amer. Math. Soc. 185, 237-251(1973). (pdf)
 [39] "Bifurcation in the presence of a symmetry group." Archive Rat. Mech. Anal. 51, 136-159(1973). (pdf)
 [40] "Some remarks on the location of zeroes of the partition function for lattice systems." Commun. Math. Phys. 31, 265-277(1973). (pdf)
 [41] "Some comments on chemical oscillations." Trans. N.Y. Acad. Sci. 35, 66-71(1973).
 [42] (with R. Bowen) "The ergodic theory of Axiom A flows." Inventiones Math. 29, 181-202(1975). (pdf)
 [43] (with D. Sullivan) "Currents, flows and diffeomorphisms." Topology 14, 319-327(1975). (pdf)
 [44] "Generalized zeta-functions for Axiom A basic sets"." Bull. Amer. Math. Soc. 82, 153-156 (1976). (pdf)
 [45] "Zeta functions for expanding maps and Anosov flows." Inventiones Math. 34, 231-242(1976). (pdf)
 [46] "A measure associated with Axiom A attractors." Am. J. Math. 98, 619-654(1976). (pdf)
 [47] "Probability estimates for continuous spin systems." Commun. Math. Phys. 50, 189-194(1976). (pdf)
 [48] "On manifolds of phase coexistence." (in Russian) Teor. Mat. Fiz. 30 No 1, 40-47(1977). (pdf)
 [49] "A heuristic theory of phase transitions." Commun. Math. Phys. 53, 195-208(1977). (pdf)
 [50] "Applications conservant une mesure absolument continue par rapport à $dx$ sur $[0,1]$." Commun. Math. Phys. 55,47-51(1977). (pdf)
 [51] "An inequality for the entropy of differentiable maps." Bol. Soc. Bras. Mat. 9, 83-87(1978). (pdf)
 [52] (with S. Newhouse and F. Takens) "Occurrence of strange Axiom A attractors near quasi-periodic flows on $T^m$, $m\ge3$." Commun. Math. Phys. 64, 35-40(1978). (pdf)
 [53] "Integral representation of measures associated with a foliation." Publ. Math. IHES 48, 127-132(1978). (pdf)
 [54] "Invariant measures for a diffeomorphism which expands the leaves of a foliation." Publ. Math. IHES 48, 133-135(1978). (pdf)
 [55] "Sensitive dependence on initial condition and turbulent behavior of dynamical systems." Ann. N.Y. Acad. Sci. 316, 408-416(1978). (pdf)
 [56] "What are the measures describing turbulence?" Progr. Theoret. Phys. Suppl. 64, 339-345(1978). (pdf)
 [57] "Analyticity properties of the characteristic exponents of random matrix products." Advances Math. 32, 68-80(1979). (pdf)
 [58] "Microscopic fluctuations and turbulence." Phys. Letters 72 A, 81-82(1979). 
 [59] "Ergodic theory of differentiable dynamical systems." Publ. Math. IHES 50, 27-58(1979). (pdf)
 [60] "Study of a simplexial complex related to the Wightman functions." Bull. Soc. Math. de Belgique 31, 157-169(1979).
 [61] (with M. Shub) "Stable manifolds for maps." pp. 389-392 in Global theory of dynamical systems, Lecture Notes in Math. No 819, Springer, Berlin, 1980. (pdf)
 [62] "Les attracteurs étranges." La Recherche 11, 132-144(1980).
 [63] "Strange attractors." (English translation of the above) Math. Intelligencer 2, 126-137(1980).
 [64] "Measures describing a turbulent flow." Ann. N.Y. Acad. Sci. 357,1-9(1980). (pdf)
 [65] "Small random perturbations of dynamical systems and the definition of attractors." Commun. Math. Phys. 82, 137-151(1981). (pdf)
 [66] "Must thermodynamic functions be piecewise analytic?" J. Statist. Phys. 26, 397-399(1981). (pdf)
 [67] "Differentiable dynamical systems and the problem of turbulence." Bull. Amer. Math. Soc. 5, 29-42(1981).
 [68] "The pressure of the geodesic flow on a negatively curved manifold." Bol. Soc. Bras. Mat. 12, 95-100(1981). (pdf)
 [69] "Characteristic exponents and invariant manifolds in Hilbert space." Ann. of Math. 115, 243-290(1982). (pdf)
 [70] (with M. Campanino and H. Epstein) "On Feigenbaum's functional equation $g\circ g(\lambda x)+\lambda g(x)=0$." Topology 21, 125-129(1982). (pdf)
 [71] "Do turbulent crystals exist?" Physica 113 A, 619-623(1982).
 [72] (with J. Fröhlich) "Statistical mechanics of vortices in an inviscid two-dimensional fluid." Commun. Math. Phys. 87, 1-36(1982). (pdf)
 [73] "Large volume limit of the distribution of characteristic exponents in turbulence." Commun. Math. Phys. 87, 287-302(1982). (pdf)
 [74] "Repellers for real analytic maps." Ergod. Theor. Dynam. Syst. 2, 99-107(1982). pdf
 [75] "Flots qui ne mélangent pas exponentiellement." C. R. Acad. Sci. Paris Ser. I 296, 191-193(1983). (pdf)
 [76] (with E. Marinari, G. Parisi and P. Windey) "Random walk in a random environment and $1/f$ noise." Phys. Rev. Letters 50, 1223-1225(1083). (pdf)
 [77] (with E. Marinari, G. Parisi and P. Windey) "On the interpretation of $1/f$ noise." Commun. Math. Phys. 89, 1-12(1983). (pdf)
 [78] "Characteristic exponents for a viscous fluid subjected to time dependent forces." Commun. Math. Phys. 93, 285-300(1984). (pdf)
 [79] "Rotation numbers for diffeomorphisms and flows." Ann. Inst. Henri Poincaré 42, 109-115(1985). (pdf)
 [80] (with J.-P. Eckmann) "Two-dimensional Poiseuille flow." Physica Scripta T 9, 153-154(1985).
 [81] (with J.-P. Eckmann) "Ergodic theory of chaos and strange attractors." Rev. Mod. Phys. 57, 617-656(1985). (pdf)
 [82] "Resonances of chaotic dynamical systems." Phys. Rev. Letters 56, 405-407 (1986). (pdf)
 [83] (with N. Kopell) "Bounds on complexity in reaction-diffusion systems." SIAM J. Appl. Math. 46, 68-80(1986). (pdf)
 [84] "Locating resonances for Axiom A dynamical systems." J. Statist. Phys. 44, 281-292(1986).
 [85] (with Ya.G. Sinai) From dynamical systems to statistical mechanics and back." Physica 140 A, 1-8(1986)
 [86] (with J.-P. Eckmann and S. Oliffson Kamphorst) "Lyapunov exponents from time series." Phys. Rev A 34, 4971-4979(1986). (pdf)
 [87] "A mathematical reformulation of Derrida's REM and GREM." Commun. Math. Phys. 108, 225-239(1987). (pdf)
 [88] "One-dimensional Gibbs states and Axiom A diffeomorphisms." J. Differential Geometry. 25, 117-137(1987).
 [89] "Resonances for Axiom A flows." J. Differential Geometry. 25, 99-116(1987). (pdf)
 [90] (with M. Aizenman and J.L. Lebowitz) "Some rigorous results on the Sherrington-Kirkpatrick spin glass model." Commun. Math. Phys. 112, 3-20(1987). (pdf)
 [91] "Diagnosis of dynamical systems with fluctuating parameters." Proc. R. Soc. London. A 413, 5-8(1987).
 [92] (with J.-P. Eckmann and S. Oliffson Kamphorst) "Recurrence plots of dynamical systems." Europhysics Letters 4, 973-977(1987). (pdf)
 [93] "Non-commutative algebras for hyperbolic diffeomorphisms." Inventiones Math. 93, 1-13(1988). (pdf)
 [94] "Is our mathematics natural? The case of equilibrium statistical mechanics." Bull. Amer. Math. Soc. 19, 259-268(1988). (pdf)
 [95] (with H. Epstein) "Test of a probabilistic model of evolutionary success." Physics Reports 184, 289-292(1989). (pdf)
 [96] (with V. Baladi and J.-P. Eckmann) "Resonances for intermittent systems." Nonlinearity 2, 119-135(1989). (pdf)
 [97] "Une extension de la théorie de Fredholm." C. R. Acad. Sci. Paris Ser. I 309, 309-310(1989).
 [98] "The thermodynamic formalism for expanding maps." Commun. Math. Phys. 125, 239-262(1989). (pdf)
 [99] "Deterministic chaos: the science and the fiction." Proc. R. Soc. London. A 427, 241-248(1990). (pdf)
 [100] "An extension of the theory of Fredholm determinants." Publ. Math. IHES 72, 175-193(1990). (pdf)
 [101] "Is there screening in turbulence?" J. Statist. Phys. 61, 865-868(1990). (pdf)
 [102] "Spectral properties of a class of operators associated with maps in one dimension." Ergod. Theor. Dynam. Syst. 11, 757-767(1991). (pdf)
 [103] "Spectral properties of a class of operators associated with conformal maps in two dimensions." Commun. Math. Phys. 144, 537-556(1992). (pdf)
 [104] (with N.T.A. Haydn) "Equivalence of Gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specification." Commun. Math. Phys. 148, 155-167(1992). (pdf)
 [105] "Dynamical zeta functions: where do they come from and what are they good for?" pp. 43-51 in Mathematical Physics X (ed. K.Schmüdgen) Springer, Berlin, 1992. (pdf)
 [106] (with J.-P. Eckmann) "Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems." Physica B 56, 185-187(1992). (pdf)
 [107] "Thermodynamic formalism for maps satisfying positive expansiveness and specification." Nonlinearity 5, 1223-1226(1992) (pdf)
[108] "Analytic completions for dynamical zeta functions." Helv. Phys. Acta 66, 181-191(1993). (pdf)
 [109] "Dynamical zeta functions for maps of the interval." Bull. Amer. Math. Soc. (NS) 30, 212-214(1994). (pdf)
 [110] "Where can one hope to profitably apply the ideas of chaos?" Physics Today 47 No 7, 24-30(1994). (pdf)
 [111] (with V. Baladi) "An extension of the theory of Milnor and Thurston on the zeta functions of interval maps." Ergod. Th. and Dynam. Syst. 14, 621-632(1994). (pdf)
 [112] "Functional equation for dynamical zeta functions of Milnor-Thurston type." Commun. Math. Phys. 175, 63-88(1996).(pdf)
 [113] (with V. Baladi) "Sharp determinants" Invent. Math. 123, 553-574(1996). (pdf)
 [114] "Positivity of entropy production in nonequilibrium statistical mechanics." J. Satist. Phys. 85, 1-23(1996). (ps - pdf)
 [115] "Positivity of entropy production in the presence of a random thermostat" J. Statist. Phys. 86, 935-951(1997). (ps - pdf)
 [116] "Differentiation of SRB states." Commun. Math. Phys. 187,227-241(1997). (PS - pdf)
 [117] "Entropy production in nonequilibrium statistical mechanics" Commun. Math. Phys. 189, 365-371(1997). (ps - pdf)
 [118] (with G. Gallavotti) "SRB states and nonequilibrium statistical mechanics close to equilibrium" Commun. Math. Phys. 190, 279-285(1997). (ps - pdf)
 [119] (with V. Baladi, A. Kitaev and S. Semmes) "Sharp determinants and kneading operators for holomorphic maps" Proc. Steklov Inst. Math. 216, 193-235(1997). (pdf)
 [120] "Nonequilibrium statistical mechanics near equilibrium: computing higher order terms." Nonlinearity 11, 5-18(1998). (ps - pdf)
 [121] "General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium." Phys. Letters A 245, 220-224\ (1998). (ps - pdf)
 [122] "Zeros of graph-counting polynomials." Commun. Math. Phys. 200, 43-56 (1999). (ps - pdf)
 [123] "Counting unbranched subgraphs." J. Algebraic Combinatorics 9, 157-160(1999). (ps - pdf)
 [124] "Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics." J. Statist. Phys. 95, 393-468(1999). (ps - pdf)
 [125] "Natural nonequilibrium states in quantum statistical mechanics." J. Statist. Phys. 98, 57-75(2000). (ps - pdf)
 [126] "Conversations on mathematics with a visitor from outer space." pp. 251-259 in Mathematics: Frontiers and Perspectives, edited by V. Arnold, M. Atiyah, P. Lax and B. Mazur, Amer. Math. Soc. (for IMU),2000. (ps - pdf)
 [127] "Mathematical Platonism reconsidered." Nieuw Archief voor Wiskunde 5/1, 30-33(2000). (ps - pdf)
 [128] "A remark on the equivalence of isokinetic and isoenergetic thermostats in the thermodynamic limit." J. Statist. Phys. 100, 757-763(2000). (ps - pdf)
 [129] "Chaos, imprédictibilité et hasard." pp. 647-656 in Qu'est-ce que l'Univers? éd. Y. Michaud, Odile Jacob, Paris, 2000. (ps - pdf)
 [130] "Chaos: here be no dragons." Nature 411 no. 6833, 27(2001). (ps - pdf)
 [131] "Historical behaviour in smooth dynamical systems." pp. 63-66 Global analysis of dynamical systems edited by H. Broer, B. Krauskopf and G. Vegter, Institute of Physics, London, 2001. (ps - pdf)
 [132] (with A. Wilkinson) "Absolutely singular dynamical foliations. " Commun. Math. Phys. 219, 481-487(2001). (ps - pdf)
 [133] "A departure from equilibrium." Nature 414 no. 6861, 263-264(2001).
 [134] "Entropy production in quantum spin systems." Commun. Math. Phys. 224, 3-16(2001). (ps - pdf)
 [135] "How should one define entropy production for nonequilibrium quantum spin systems?'' Rev. Math. Phys. 14,701-707(2002). (ps - pdf)
 [136] "Some ill-defined problems on regular and messy problems in statistical mechanics and smooth dynamics for which I would like the advice of Yasha Sinai.'' J. Statist. Phys. 108,723-728(2002). (ps - pdf)
 [137] "Dynamical zeta functions and transfer operators.''
Notices Amer. Math. Soc. 49,887-895(2002). (ps - pdf)
 [138] "Grace-like polynomials." in Foundations of computational mathematics. Proceedings of Smalefest 2000 edited by F. Cucker and J.M. Rojas, World Scientific, Singapore, 2002. (ps - pdf)

[139] "Differentiation of SRB states: correction and complements."
Commun. Math. Phys. 234, 185-190(2003). (ps - pdf)
 [140] "Extending the definition of entropy to nonequilibrium steady states."
Proc. Nat. Acad. Sci. 100,30054-3058(2003). (ps - pdf)
 [141] "Perturbation theory for Lyapunov exponents of a toral map: extension of a result of Shub and Wilkinson". Israel J. Math. 134, 345-361 (2003). (ps - pdf)

[142] "Conversations on nonequilibrium physics with an extraterrestrial." Physics Today 57 No 5, 48-53 (2004).

[143] "Application of hyperbolic dynamics to physics: some problems and conjectures." Bull. Amer. Math. Soc. (N.S) 41, 275-278 (2004). (ps - pdf)
[144] "Differentiating the absolutely contimuous invariant measure of an interval map f with respect to f." Commun. Math. Phys. 258, 445-453 (2005). (ps - pdf)

[145] (with Y. Jiang) "Analyticity of the susceptibility function for unimodal Markovian maps of the interval." Nonlinearity 18, 2447-2453 (2005). (ps - pdf)

[146] "What is a strange attractor ?" Notices of the AMS 53, 764-765 (2006).(ps - pdf)

[147] "Nonequilibrium statistical mechanics and entropy production in a classical infinite system of rotators." Commun. Math. Phys. 270, 233-265 (2007). (ps - pdf)

[148] "Differentiation of SRB states for hyperbolic flows." Ergod. Theor. Dynam. Syst. 28, 613-631 (2008). (ps - pdf)

[149] What physical quantities make sense in nonequilibrium statistical mechanics? pp89-97 - Boltzmann's legacy edited by Gallavotti, W.L. Reiter, and J. Yngvason, European Mathematial Society, Zürich, 2008. (ps - pdf)

[150] "Structure anf f-dependence of the a.c.i.m. for unimodal map f of Misiurewicz type" Commun. Math. Phys. 287, 1039-1070 (2009). (ps - pdf)

[151] "A review of linear response theory for general differentiable dynamical systems." Nonlinearity 22, 855-870 (2009). (ps - pdf)

[152] "Characterization of Lee-Yang polynomials." Annals of Math. 171, 589-603 (2010) (ps - pdf)

[153] "La théorie ergodique des systèmes dynamiques d'Anosov". PP. 195-226 inLeçons de mathématiques d'aujourd'hui vol 4 (ed F. Bayart et E. Charpentier) Cassini, Paris, 2010. (pdf)

[154] "Singularities of the susceptibility of an SRB measure in the presence of stable-unstable tangencies" Phil. Trans. R. Soc. A 369, 482-493 (2011). (ps - pdf)

[155] (with J.L. Lebowitz) "Phase transitions with four-spin interactions." Commun. Math. Phys. 304, 711-722 (2011). (ps - pdf)

[156] "A mechanical model for Fourier's law of heat conduction". Commun. Math. Phys. 311, 755-768 (2012) (ps - pdf)

(with J.L. Lebowitz and E.R. Speer) "Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems." J. Math. Phys. 53, 095211(1-13)(2012)( pdf)

"Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics." Proc. Nat. Acad. Sci. 109, 20344-20346 (2012) (ps - pdf)

"Post-human mathematics." arXiv:1308.4678 (2013) (ps - pdf)

[160] "Nonequilibrium: from heat transport to turbulence (to life)." Physik Journal 13 No 8/37-40 (2014) (ps - pdf)

[161] "Non-equilibrium statistical mechanics of turbulence." J. Statist. Phys. 157, 205-218 (2014) (ps - pdf)

[162] "Biology and nonequilibrium: remarks on a paper by J.P. England." Eur. Phys. J. Special Topics 224,935-944(2015).

[163] (with J.L. Lebowitz, B. Pittel and E.R. Speer) "Central limit theorems, Lee-Yang zeros, and graph-counting polynomials." J. Combin. Theory Ser. A bf 142,147-183(2016). (arXiv:1408.4153v2).

[164] "Hydrodynamic turbulence as a nonstandard transport phenomenom." Chapter 3 (pp 49-57) in Chr. Skiadas (editor) The foundation of chaos revisited: from Poincaré to recent advancements. Spronger, Heidelberg, 2016.

[165] "A generalized detailed balance relation." J. Statist. Phus. 164,463-471(2016). (arXiv:1510.08357v2).

  * Less original material from conference proceedings, etc. has been omitted.


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