## Ruelle, David Pierre

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 Author ID: ruelle.david-pierre Published as: Ruelle, David; Ruelle, D.; Ruelle, David Pierre; Ruelle, David P. more...less Homepage: http://www.ihes.fr/~ruelle/ External Links: MGP · ORCID · Wikidata · Math-Net.Ru · dblp · GND · IdRef
 Documents Indexed: 174 Publications since 1958, including 13 Books 1 Contribution as Editor · 6 Further Contributions Biographic References: 3 Publications Co-Authors: 53 Co-Authors with 35 Joint Publications 2,086 Co-Co-Authors
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### Co-Authors

 138 single-authored 5 Eckmann, Jean-Pierre 4 Baladi, Viviane 4 Hepp, Klaus 4 Lebowitz, Joel Louis 3 Bergé, Pierre 3 Pomeau, Yves 3 Takens, Floris 3 Vidal, Christian 2 Borzacchini, Luigi 2 Glimm, James G. 2 Jaffe, Arthur Michael 2 Lanford, Oscar E. III 2 Speer, Eugene R. 1 Aizenman, Michael 1 Araki, Huzihiro 1 Atiyah, Michael Francis 1 Borel, Armand 1 Bowen, Rufus 1 Campanino, Massimo 1 Chaitin, Gregory John 1 Dell’Antonio, C.-F. 1 DeWitt-Morette, Cécile 1 Doplicher, Sergio 1 Epstein, Henri 1 Friedan, Daniel Harry 1 Fröhlich, Jürg Martin 1 Fröhling, Jüerg 1 Gallavotti, Giovanni M. 1 Ginibre, Jean 1 Glaser, Vladimir Jurko 1 Gray, Jeremy John 1 Griffiths, Robert B. 1 Guerra, Francesco 1 Haydn, Nicolai T. A. 1 Hirsch, Morris W. 1 Isola, Stefano 1 Jiang, Yunping 1 Jost, Res 1 Kopell, Nancy J. 1 Lieb, Elliott H. 1 Mac Lane, Leslie Saunders 1 Mandelbrot, Benoit B. 1 Marinari, Enzo 1 N. Stehlíková 1 Nappi, Chiara R. 1 Nelson, Joseph Edward 1 Newhouse, Sheldon E. 1 Parisi, Giorgio 1 Pittel, Boris G. 1 Robinson, Derek W. 1 Rugh, Hans Henrik 1 Schwarz, Albert S. 1 Semmes, Stephen W. 1 Shub, Michael 1 Simon, Barry 1 Sinaĭ, Yakov Grigor’evich 1 Steinmann, Othmar 1 Stora, Raymond 1 Straeter, Ray 1 Strocchi, Franco 1 Sullivan, Dennis Parnell 1 Thom, René 1 Uhlenbeck, Karen Keskulla 1 Velo, Giorgio 1 Wilkinson, Amie 1 Windey, Paul 1 Witten, Edward 1 Zeeman, Erik Christopher
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### Serials

 35 Communications in Mathematical Physics 13 Journal of Statistical Physics 8 Helvetica Physica Acta 6 Nonlinearity 5 Bulletin of the American Mathematical Society. New Series 4 Journal of Mathematical Physics 4 Publications Mathématiques 4 Inventiones Mathematicae 4 Ergodic Theory and Dynamical Systems 3 Notices of the American Mathematical Society 3 Collection Enseignement des Sciences 2 Reviews of Modern Physics 2 Boletim da Sociedade Brasileira de Matemática 2 Journal of Differential Geometry 2 Topology 2 Physica D 2 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Annals of Mathematics. Second Series 2 Bulletin of the American Mathematical Society 1 Archive for Rational Mechanics and Analysis 1 Israel Journal of Mathematics 1 Mathematical Biosciences 1 Physica A 1 Physics Letters. A 1 Reviews in Mathematical Physics 1 The Mathematical Intelligencer 1 Advances in Mathematics 1 American Journal of Mathematics 1 Journal of Combinatorial Theory. Series A 1 Journal of Functional Analysis 1 Transactions of the American Mathematical Society 1 Bulletin de la Classe des Sciences. 5e Série 1 Pokroky Matematiky, Fyziky & Astronomie 1 Proceedings of the National Academy of Sciences of the United States of America 1 SIAM Journal on Applied Mathematics 1 Bulletin de la Société Mathématique de Belgique. Série A 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Indagationes Mathematicae. New Series 1 Journal of Algebraic Combinatorics 1 European Mathematical Society Newsletter 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Annales Henri Poincaré 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 Physica Scripta 1 Nuclear Physics 1 Il Nuovo Cimento, X. Series 1 CRM Monograph Series 1 Encyclopedia of Mathematics and Its Applications 1 World Scientific Series on Nonlinear Science. Series A 1 La Scienza Nuova 1 Cambridge Mathematical Library 1 Memorabili
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### Fields

 91 Dynamical systems and ergodic theory (37-XX) 49 Statistical mechanics, structure of matter (82-XX) 21 Fluid mechanics (76-XX) 16 Measure and integration (28-XX) 15 General and overarching topics; collections (00-XX) 14 Probability theory and stochastic processes (60-XX) 12 Global analysis, analysis on manifolds (58-XX) 9 History and biography (01-XX) 8 Operator theory (47-XX) 8 General topology (54-XX) 7 Quantum theory (81-XX) 4 Combinatorics (05-XX) 4 Functions of a complex variable (30-XX) 4 Functional analysis (46-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Manifolds and cell complexes (57-XX) 2 Mathematical logic and foundations (03-XX) 2 Ordinary differential equations (34-XX) 1 Number theory (11-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

143 Publications have been cited 6,799 times in 5,012 Documents Cited by Year
Ergodic theory of chaos and strange attractors. Zbl 0989.37516
Eckmann, J. P.; Ruelle, D.
1985
Statistical mechanics. Rigorous results. Zbl 0177.57301
Ruelle, David
1969
On the nature of turbulence. Zbl 0223.76041
Ruelle, David; Takens, Floris
1971
The ergodic theory of axiom A flows. Zbl 0311.58010
Bowen, Rufus; Ruelle, David
1975
Thermodynamic formalism. The mathematical structures of classical equilibrium. Statistical mechanics. With a foreword by Giovanni Gallavotti. Zbl 0401.28016
Ruelle, David
1978
Ergodic theory of differentiable dynamical systems. Zbl 0426.58014
Ruelle, David
1979
Superstable interactions in classical statistical mechanics. Zbl 0198.31101
Ruelle, D.
1970
A measure associated with axiom-A attractors. Zbl 0355.58010
Ruelle, David
1976
An inequality for the entropy of differentiable maps. Zbl 0432.58013
Ruelle, David
1978
Repellers for real analytic maps. Zbl 0506.58024
Ruelle, David
1982
Thermodynamic formalism. The mathematical structures of equilibrium statistical mechanics. 2nd edition. Zbl 1062.82001
Ruelle, David
2004
Statistical mechanics of a one-dimensional lattice gas. Zbl 0165.29102
Ruelle, D.
1968
Characteristic exponents and invariant manifolds in Hilbert space. Zbl 0493.58015
Ruelle, David
1982
Zeta-functions for expanding maps and Anosov flows. Zbl 0329.58014
Ruelle, David
1976
Statistical mechanics. Rigorous results. Zbl 1016.82500
Ruelle, David
1999
Occurrence of strange Axiom A attractors near quasi periodic flows on $$T^m$$, $$m\geq 3$$. Zbl 0396.58029
Newhouse, S.; Ruelle, D.; Takens, F.
1978
Elements of differentiable dynamics and bifurcation theory. Zbl 0684.58001
Ruelle, David
1989
Note concerning our paper ”On the nature of turbulence”. Commun. math. Phys. 20, 167-192 (1971). Zbl 0227.76084
Ruelle, D.; Takens, F.
1971
Statistical mechanics on a compact set with Z$$^\nu$$ action satisfying expansiveness and specification. Zbl 0278.28012
Ruelle, David
1974
Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. Zbl 0934.37010
Ruelle, David
1999
Differentiation of SRB states. Zbl 0895.58045
Ruelle, David
1997
The thermodynamic formalism for expanding maps. Zbl 0702.58056
Ruelle, David
1989
Currents, flows and diffeomorphisms. Zbl 0321.58019
Ruelle, David; Sullivan, Dennis
1975
Some remarks on the ground state of infinite systems in statistical mechanics. Zbl 0169.57502
Ruelle, D.
1969
Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Zbl 1108.82312
Aizenman, M.; Lebowitz, J. L.; Ruelle, D.
1987
A mathematical reformulation of Derrida’s REM and GREM. Zbl 0617.60100
Ruelle, David
1987
Positivity of entropy production in nonequilibrium statistical mechanics. Zbl 0973.37014
Ruelle, David
1996
Analycity properties of the characteristic exponents of random matrix products. Zbl 0426.58018
Ruelle, D.
1979
A review of linear response theory for general differentiable dynamical systems. Zbl 1158.37305
Ruelle, David
2009
Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Zbl 0759.58030
Eckmann, J.-P.; Ruelle, D.
1992
Mean entropy of states in classical statistical mechanics. Zbl 0144.48205
Robinson, D. W.; Ruelle, D.
1967
Bifurcations in the presence of a symmetry group. Zbl 0259.58009
Ruelle, David
1973
Characteristic exponents for a viscous fluid subjected to time dependent forces. Zbl 0565.76031
Ruelle, David
1984
General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium. Zbl 0940.82035
Ruelle, David
1998
Natural nonequilibrium states in quantum statistical mechanics. Zbl 0988.82032
Ruelle, David
2000
An extension of the theory of Fredholm determinants. Zbl 0732.47003
Ruelle, David
1990
Small random perturbations of dynamical systems and the definition of attractors. Zbl 0482.58017
Ruelle, David
1981
On the asymptotic condition in quantum field theory. Zbl 0158.45702
Ruelle, D.
1962
Chaotic evolution and strange attractors. The statistical analysis of time series for deterministic nonlinear systems. Notes prepared by Stefano Isola from the ‘Lezioni Lincee’ (Rome, May 1987). Zbl 0683.58001
Ruelle, David
1989
Applications conservant une mesure absolument continue par rapport à $$dx$$ sur $$[0,1]$$. Zbl 0362.28013
Ruelle, D.
1977
Noncommutative algebras for hyperbolic diffeomorphisms. Zbl 0657.58026
Ruelle, David
1988
State of physical systems. Zbl 0141.44604
Ruelle, D.
1966
L’ordre dans le chaos. Vers une approche déterministe de la turbulence. (Order within chaos; towards a deterministic approach to turbulence). Préface de David Ruelle. Zbl 0669.58022
Bergé, Pierre; Pomeau, Yves; Vidal, Christian
1984
Dynamical zeta functions for piecewise monotone maps of the interval. Zbl 0805.58006
Ruelle, David
1994
Generalized zeta-functions for axiom A basic sets. Zbl 0316.58016
Ruelle, D.
1976
Large volume limit of the distribution of characteristic exponents in turbulence. Zbl 0546.76083
Ruelle, David
1982
Locating resonances for axiom A dynamical systems. Zbl 0655.58026
Ruelle, David
1986
Absolutely singular dynamical foliations. Zbl 1031.37029
Ruelle, David; Wilkinson, Amie
2001
SRB states and nonequilibrium statistical mechanics close to equilibrium. Zbl 0909.60091
Gallavotti, Giovanni; Ruelle, David
1997
Strange attractors. Zbl 0487.58014
Ruelle, David
1980
Deterministic chaos: The science and the fiction. Zbl 0702.58042
Ruelle, D.
1990
Integral representations of invariant states on $$B^ *$$-algebras. Zbl 0166.11402
Lanford, O.; Ruelle, D.
1967
Entropy production in quantum spin systems. Zbl 1051.82003
Ruelle, David
2001
Historical behaviour in smooth dynamical systems. Zbl 1067.37501
Ruelle, David
2001
Dynamical zeta functions and transfer operators. Zbl 1126.37305
Ruelle, David
2002
Flots qui ne mélangent pas exponentiellement. Zbl 0531.58040
Ruelle, David
1983
Statistical mechanics of vortices in an inviscid two-dimensional fluid. Zbl 0505.76037
Fröhlich, Jürg; Ruelle, David
1982
Nonequilibrium statistical mechanics near equilibrium: Computing higher-order terms. Zbl 0896.58071
Ruelle, David
1998
Resonances for axiom A flows. Zbl 0658.58026
Ruelle, D.
1987
Equivalence of Gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specification. Zbl 0763.54028
Haydn, N. T. A.; Ruelle, D.
1992
A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule. Zbl 0154.46502
Ruelle, D.
1967
Thermodynamic formalism for maps satisfying positive expansiveness and specification. Zbl 0772.58047
Ruelle, David
1992
Differentiating the absolutely continuous invariant measure of an interval map $$f$$ with respect to $$f$$. Zbl 1080.37046
Ruelle, David
2005
Connection between Wightman functions and Green functions in $$p$$-space. Zbl 0097.43003
Ruelle, D.
1961
Differentiation of SRB states for hyperbolic flows. Zbl 1165.37011
Ruelle, David
2008
Correlation functionals. Zbl 0127.21501
Ruelle, D.
1965
Extending the definition of entropy to nonequilibrium steady states. Zbl 1063.82020
Ruelle, David P.
2003
A theorem on canonical commutation and anticommutation relations. Zbl 0178.58001
Dell’Antonio, C.-F.; Doplicher, S.; Ruelle, D.
1966
On Feigenbaum’s functional equation gg(lambdax)+lambdag(x)=0. Zbl 0513.58034
Campanino, M.; Epstein, H.; Ruelle, D.
1982
Differentiation of SRB states: Correction and complements. Zbl 1019.37014
Ruelle, David
2003
Central limit theorems, Lee-Yang zeros, and graph-counting polynomials. Zbl 1334.05065
Lebowitz, J. L.; Pittel, B.; Ruelle, D.; Speer, E. R.
2016
An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps. Zbl 0818.58013
Baladi, V.; Ruelle, D.
1994
Characterization of Lee-Yang polynomials. Zbl 1251.30005
Ruelle, David
2010
Rotation numbers for diffeomorphisms and flows. Zbl 0556.58026
Ruelle, David
1985
States of classical statistical mechanics. Zbl 0154.46503
Ruelle, D.
1967
Some remarks on the location of zeroes of the partition function for lattice systems. Zbl 1125.82311
Ruelle, David
1973
Differentiable dynamical systems and the problem of turbulence. Zbl 0474.76052
Ruelle, David
1981
Statistical mechanics on a compact set with Z$$^\nu$$ action satisfying expansiveness and specification. Zbl 0255.28015
Ruelle, David
1972
Turbulence, strange attractors, and chaos. Zbl 0922.76009
1995
Classical statistical mechanics of a system of particles. Zbl 0113.45606
Ruelle, D.
1963
Integral representation of states on a $$C^*$$-algebra. Zbl 0196.14902
Ruelle, D.
1970
Application of hyperbolic dynamics to physics: some problems and conjectures. Zbl 1102.37051
Ruelle, David
2004
Structure and $$f$$-dependence of the a.c.i.m. for a unimodal map $$f$$ of Misiurewicz type. Zbl 1202.37008
Ruelle, David
2009
Measures describing a turbulent flow. Zbl 0474.76056
Ruelle, David
1980
Entropy production in nonequilibrium statistical mechanics. Zbl 0888.60082
Ruelle, David
1997
Resonances for intermittent systems. Zbl 0673.58030
Baladi, V.; Eckmann, J.-P.; Ruelle, D.
1989
Is our mathematics natural? The case of equilibrium statistical mechanics. Zbl 0649.00028
Ruelle, David
1988
Analycity of the susceptibility function for unimodal Markovian maps of the interval. Zbl 1089.37020
Jiang, Yunping; Ruelle, David
2005
Bounds on complexity in reaction-diffusion systems. Zbl 0596.35065
Kopell, Nancy; Ruelle, David
1986
Zeros of graph-counting polynomials. Zbl 0917.05074
Ruelle, David
1999
Counting unbranched subgraphs. Zbl 0915.05068
Ruelle, David
1999
One-dimensional Gibbs states and Axiom A diffeomorphisms. Zbl 0628.58043
Ruelle, D.
1987
Responses to “Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics”, by A. Jaffe and F. Quinn. Zbl 0803.01014
Atiyah, Michael; Borel, Armand; Chaitin, G. J.; Friedan, Daniel; Glimm, James; Gray, Jeremy J.; Hirsch, Morris W.; MacLane, Saunders; Mandelbrot, Benoit B.; Ruelle, David; Schwarz, Albert; Uhlenbeck, Karen; Thom, René; Witten, Edward; Zeeman, Christopher
1994
Stable manifolds for maps. Zbl 0453.58018
Ruelle, David; Shub, Michael
1980
On the interpretation of 1/f noise. Zbl 0532.60062
Marinari, E.; Parisi, G.; Ruelle, D.; Windey, P.
1983
On the asymptotic behaviour of Wightman functions in space-like directions. Zbl 0161.23503
Araki, H.; Hepp, K.; Ruelle, D.
1962
Dynamical systems with turbulent behavior. Zbl 0452.34038
Ruelle, David
1978
The Lorenz attractor and the problem of turbulence. Zbl 0355.76036
Ruelle, David
1976
Phase transitions with four-spin interactions. Zbl 1219.82080
Lebowitz, Joel L.; Ruelle, David
2011
A mechanical model for Fourier’s law of heat conduction. Zbl 1246.82075
Ruelle, David
2012
Linear response theory for diffeomorphisms with tangencies of stable and unstable manifolds – a contribution to the Gallavotti-Cohen chaotic hypothesis. Zbl 1408.37044
Ruelle, David
2018
Central limit theorems, Lee-Yang zeros, and graph-counting polynomials. Zbl 1334.05065
Lebowitz, J. L.; Pittel, B.; Ruelle, D.; Speer, E. R.
2016
A generalized detailed balance relation. Zbl 1348.82070
Ruelle, David
2016
Non-equilibrium statistical mechanics of turbulence. Zbl 1307.82016
Ruelle, David
2014
A mechanical model for Fourier’s law of heat conduction. Zbl 1246.82075
Ruelle, David
2012
Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems. Zbl 1322.82004
Lebowitz, Joel L.; Ruelle, David; Speer, Eugene R.
2012
Phase transitions with four-spin interactions. Zbl 1219.82080
Lebowitz, Joel L.; Ruelle, David
2011
Singularities of the susceptibility of a Sinai-Ruelle-Bowen measure in the presence of stable-unstable tangencies. Zbl 1230.37044
Ruelle, David
2011
Characterization of Lee-Yang polynomials. Zbl 1251.30005
Ruelle, David
2010
A review of linear response theory for general differentiable dynamical systems. Zbl 1158.37305
Ruelle, David
2009
Structure and $$f$$-dependence of the a.c.i.m. for a unimodal map $$f$$ of Misiurewicz type. Zbl 1202.37008
Ruelle, David
2009
Differentiation of SRB states for hyperbolic flows. Zbl 1165.37011
Ruelle, David
2008
What physical quantities make sense in nonequilibrium statistical mechanics. Zbl 1156.82300
Ruelle, David
2008
Nonequilibrium statistical mechanics and entropy production in a classical infinite system of rotators. Zbl 1119.82036
Ruelle, David
2007
The mathematician’s brain. Zbl 1131.00001
Ruelle, David
2007
What is…a strange attractor? Zbl 1137.37012
Ruelle, David
2006
Differentiating the absolutely continuous invariant measure of an interval map $$f$$ with respect to $$f$$. Zbl 1080.37046
Ruelle, David
2005
Analycity of the susceptibility function for unimodal Markovian maps of the interval. Zbl 1089.37020
Jiang, Yunping; Ruelle, David
2005
Thermodynamic formalism. The mathematical structures of equilibrium statistical mechanics. 2nd edition. Zbl 1062.82001
Ruelle, David
2004
Application of hyperbolic dynamics to physics: some problems and conjectures. Zbl 1102.37051
Ruelle, David
2004
Extending the definition of entropy to nonequilibrium steady states. Zbl 1063.82020
Ruelle, David P.
2003
Differentiation of SRB states: Correction and complements. Zbl 1019.37014
Ruelle, David
2003
Perturbation theory for Lyapunov exponents of a toral map: Extension of a result of Shub and Wilkinson. Zbl 1023.37016
Ruelle, David
2003
Is there a unified theory of nonequilibrium statistical mechanics? Zbl 1138.82332
Ruelle, David
2003
Dynamical zeta functions and transfer operators. Zbl 1126.37305
Ruelle, David
2002
How should one define entropy production for nonequilibrium quantum spin systems? Zbl 1027.82027
Ruelle, David
2002
Grace-like polynomials. Zbl 1173.30304
Ruelle, David
2002
Some ill-formulated problems on regular and messy behavior in statistical mechanics and smooth dynamics for which I would like the advice of Yasha Sinai. Zbl 1124.82300
Ruelle, David
2002
Absolutely singular dynamical foliations. Zbl 1031.37029
Ruelle, David; Wilkinson, Amie
2001
Entropy production in quantum spin systems. Zbl 1051.82003
Ruelle, David
2001
Historical behaviour in smooth dynamical systems. Zbl 1067.37501
Ruelle, David
2001
Natural nonequilibrium states in quantum statistical mechanics. Zbl 0988.82032
Ruelle, David
2000
A remark on the equivalence of isokinetic and isoenergetic thermostats in the thermodynamic limit. Zbl 1055.82522
Ruelle, David
2000
Conversations on mathematics with a visitor from outer space. Zbl 1031.00001
Ruelle, David
2000
Statistical mechanics. Rigorous results. Zbl 1016.82500
Ruelle, David
1999
Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. Zbl 0934.37010
Ruelle, David
1999
Zeros of graph-counting polynomials. Zbl 0917.05074
Ruelle, David
1999
Counting unbranched subgraphs. Zbl 0915.05068
Ruelle, David
1999
General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium. Zbl 0940.82035
Ruelle, David
1998
Nonequilibrium statistical mechanics near equilibrium: Computing higher-order terms. Zbl 0896.58071
Ruelle, David
1998
Differentiation of SRB states. Zbl 0895.58045
Ruelle, David
1997
SRB states and nonequilibrium statistical mechanics close to equilibrium. Zbl 0909.60091
Gallavotti, Giovanni; Ruelle, David
1997
Entropy production in nonequilibrium statistical mechanics. Zbl 0888.60082
Ruelle, David
1997
Positivity of entropy production in the presence of a random thermostat. Zbl 0931.37002
Ruelle, David
1997
Sharp determinants and kneading operators for holomorphic maps. Zbl 0919.58008
Baladi, V.; Kitaev, A.; Ruelle, D.; Semmes, S.
1997
Positivity of entropy production in nonequilibrium statistical mechanics. Zbl 0973.37014
Ruelle, David
1996
Sharp determinants. Zbl 0856.47005
Baladi, V.; Ruelle, D.
1996
Sharp zeta functions for smooth interval maps. Zbl 0924.58016
Ruelle, D.
1996
Functional equation for dynamical zeta functions of Milnor-Thurston type. Zbl 0846.58047
Ruelle, David
1996
Turbulence, strange attractors, and chaos. Zbl 0922.76009
1995
Dynamical zeta functions for piecewise monotone maps of the interval. Zbl 0805.58006
Ruelle, David
1994
An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps. Zbl 0818.58013
Baladi, V.; Ruelle, D.
1994
Responses to “Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics”, by A. Jaffe and F. Quinn. Zbl 0803.01014
Atiyah, Michael; Borel, Armand; Chaitin, G. J.; Friedan, Daniel; Glimm, James; Gray, Jeremy J.; Hirsch, Morris W.; MacLane, Saunders; Mandelbrot, Benoit B.; Ruelle, David; Schwarz, Albert; Uhlenbeck, Karen; Thom, René; Witten, Edward; Zeeman, Christopher
1994
Dynamical zeta functions for maps of the interval. Zbl 0804.58043
Ruelle, David
1994
Analytic completion for dynamical zeta functions. Zbl 0829.58033
Ruelle, David
1993
Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Zbl 0759.58030
Eckmann, J.-P.; Ruelle, D.
1992
Equivalence of Gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specification. Zbl 0763.54028
Haydn, N. T. A.; Ruelle, D.
1992
Thermodynamic formalism for maps satisfying positive expansiveness and specification. Zbl 0772.58047
Ruelle, David
1992
Dynamical zeta functions: Where do they come from and what are they good for. Zbl 0947.37502
Ruelle, David
1992
Spectral properties of a class of operators associated with conformal maps in two dimensions. Zbl 0753.47012
Ruelle, David
1992
Spectral properties of a class of operators associated with maps in one dimension. Zbl 0811.47002
Ruelle, David
1991
An extension of the theory of Fredholm determinants. Zbl 0732.47003
Ruelle, David
1990
Deterministic chaos: The science and the fiction. Zbl 0702.58042
Ruelle, D.
1990
Elements of differentiable dynamics and bifurcation theory. Zbl 0684.58001
Ruelle, David
1989
The thermodynamic formalism for expanding maps. Zbl 0702.58056
Ruelle, David
1989
Chaotic evolution and strange attractors. The statistical analysis of time series for deterministic nonlinear systems. Notes prepared by Stefano Isola from the ‘Lezioni Lincee’ (Rome, May 1987). Zbl 0683.58001
Ruelle, David
1989
Resonances for intermittent systems. Zbl 0673.58030
Baladi, V.; Eckmann, J.-P.; Ruelle, D.
1989
Noncommutative algebras for hyperbolic diffeomorphisms. Zbl 0657.58026
Ruelle, David
1988
Is our mathematics natural? The case of equilibrium statistical mechanics. Zbl 0649.00028
Ruelle, David
1988
Some rigorous results on the Sherrington-Kirkpatrick spin glass model. Zbl 1108.82312
Aizenman, M.; Lebowitz, J. L.; Ruelle, D.
1987
A mathematical reformulation of Derrida’s REM and GREM. Zbl 0617.60100
Ruelle, David
1987
Resonances for axiom A flows. Zbl 0658.58026
Ruelle, D.
1987
One-dimensional Gibbs states and Axiom A diffeomorphisms. Zbl 0628.58043
Ruelle, D.
1987
Diagnosis of dynamical systems with fluctuating parameters. Zbl 0625.58005
Ruelle, D.
1987
Locating resonances for axiom A dynamical systems. Zbl 0655.58026
Ruelle, David
1986
Bounds on complexity in reaction-diffusion systems. Zbl 0596.35065
Kopell, Nancy; Ruelle, David
1986
From dynamical systems to statistical mechanics and back. Zbl 0668.58050
Ruelle, D.; Sinaj, Ya. G.
1986
Ergodic theory of chaos and strange attractors. Zbl 0989.37516
Eckmann, J. P.; Ruelle, D.
1985
Rotation numbers for diffeomorphisms and flows. Zbl 0556.58026
Ruelle, David
1985
Addendum: Ergodic theory of chaos and strange attractors. Zbl 1396.37043
Eckmann, J. P.; Ruelle, D.
1985
Ergodic aspects of turbulence theory. Zbl 1063.37578
Ruelle, D.
1985
Characteristic exponents for a viscous fluid subjected to time dependent forces. Zbl 0565.76031
Ruelle, David
1984
L’ordre dans le chaos. Vers une approche déterministe de la turbulence. (Order within chaos; towards a deterministic approach to turbulence). Préface de David Ruelle. Zbl 0669.58022
Bergé, Pierre; Pomeau, Yves; Vidal, Christian
1984
Flots qui ne mélangent pas exponentiellement. Zbl 0531.58040
Ruelle, David
1983
On the interpretation of 1/f noise. Zbl 0532.60062
Marinari, E.; Parisi, G.; Ruelle, D.; Windey, P.
1983
Five turbulent problems. Zbl 1194.37095
Ruelle, David
1983
Repellers for real analytic maps. Zbl 0506.58024
Ruelle, David
1982
Characteristic exponents and invariant manifolds in Hilbert space. Zbl 0493.58015
Ruelle, David
1982
Large volume limit of the distribution of characteristic exponents in turbulence. Zbl 0546.76083
Ruelle, David
1982
Statistical mechanics of vortices in an inviscid two-dimensional fluid. Zbl 0505.76037
Fröhlich, Jürg; Ruelle, David
1982
On Feigenbaum’s functional equation gg(lambdax)+lambdag(x)=0. Zbl 0513.58034
Campanino, M.; Epstein, H.; Ruelle, D.
1982
Small random perturbations of dynamical systems and the definition of attractors. Zbl 0482.58017
Ruelle, David
1981
Differentiable dynamical systems and the problem of turbulence. Zbl 0474.76052
Ruelle, David
1981
The pressure of the geodesic flow on a negatively curved manifold. Zbl 0599.58038
Ruelle, David
1981
Strange attractors. Zbl 0487.58014
Ruelle, David
1980
Measures describing a turbulent flow. Zbl 0474.76056
Ruelle, David
1980
Stable manifolds for maps. Zbl 0453.58018
Ruelle, David; Shub, Michael
1980
Ergodic theory of differentiable dynamical systems. Zbl 0426.58014
Ruelle, David
1979
Analycity properties of the characteristic exponents of random matrix products. Zbl 0426.58018
Ruelle, D.
1979
Sensitive dependence on initial condition and turbulent behavior of dynamical systems. Zbl 0438.58003
Ruelle, David
1979
...and 43 more Documents
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### Cited by 5,291 Authors

 65 Ruelle, David Pierre 56 Pollicott, Mark 41 Kondrat’yev, Yuriĭ Grygorovych 39 Barreira, Luis Manuel 36 Gallavotti, Giovanni M. 35 Young, Lai-Sang 27 Lebowitz, Joel Louis 25 Lucarini, Valerio 25 Urbański, Mariusz 23 Lopes, Artur Oscar 22 Ledrappier, François 22 Lu, Kening 21 Valls Anglés, Cláudia 20 Jørgensen, Palle E. T. 20 Pesin, Yakov Borisovich 20 Pillet, Claude-Alain 20 Varandas, Paulo 19 Baladi, Viviane 19 Mihailescu, Eugen Gh. 18 Alves, José Ferreira 18 Sharp, Richard W. 18 Yorke, James Alan 17 Cao, Yongluo 17 Kifer, Yuri 17 Procacci, Aldo 17 Viana, Marcelo 16 Araújo, Vítor 16 Fröhlich, Jürg Martin 16 Jakšić, Vojkan 15 Albeverio, Sergio A. 15 Robinson, Derek W. 14 Kutoviy, Oleksandr V. 14 Panchenko, Dmitry 14 Röckner, Michael 13 Contucci, Pierluigi 13 Pokrovskiĭ, Alexeĭ Vadimovich 12 Carroll, Thomas L. 12 Cessac, Bruno 12 Chekroun, Mickaël D. 12 de la Llave, Rafael 12 Gelfert, Katrin Grit 12 Schreiber, Sebastian J. 12 Takahasi, Hiroki 12 Wang, Qiqi 12 Zhao, Yun 11 Chen, Ercai 11 Dereudre, David 11 Gaspard, Pierre 11 Jenkinson, Oliver 11 Kuna, Tobias 11 Maes, Christian 11 Rebenko, Alexei L. 11 Sarig, Omri M. 11 Vaienti, Sandro 11 van Enter, Aernout C. D. 10 Aizenman, Michael 10 Blumenthal, Alex 10 Bollt, Erik M. 10 Chen, Guanrong 10 Climenhaga, Vaughn 10 Collet, Pierre 10 Dolgopyat, Dmitry 10 Gaeta, Giuseppe 10 Ghil, Michael 10 Gonchenko, Sergey V. 10 Iommi, Godofredo 10 Iooss, Gérard 10 Kiessling, Michael Karl-Heinz 10 Kloeden, Peter Eris 10 Kozitsky, Yuri Vasil’evich 10 Kuznetsov, Sergey P. 10 Leplaideur, Renaud 10 Lewin, Mathieu 10 Lian, Zeng 10 Melbourne, Ian 10 Mohammed, Salah-Eldin A. 10 Osada, Hirofumi 10 Sewell, Geoffrey L. 10 Weiss, Howard 10 Wolf, Christian K. 10 Yang, Dawei 10 Yang, Xiaosong 10 Zhou, Shengfan 9 Bandtlow, Oscar F. 9 Bowen, Rufus 9 Bricmont, Jean 9 Caldas, Iberê L. 9 Cassandro, Marzio 9 Daletskii, Alexei 9 Dobrushin, Roland L’vovich 9 Dybalski, Wojciech 9 Galatolo, Stefano 9 Giuliani, Alessandro 9 Lanford, Oscar E. III 9 Lieb, Elliott H. 9 Liverani, Carlangelo 9 Luzzatto, Stefano 9 Mayer, Dieter H. 9 Park, Yong Moon 9 Picco, Pierre ...and 5,191 more Authors
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### Cited in 503 Serials

 467 Journal of Statistical Physics 459 Communications in Mathematical Physics 222 Physica D 195 Ergodic Theory and Dynamical Systems 180 Chaos 140 Journal of Mathematical Physics 130 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 124 Chaos, Solitons and Fractals 82 Transactions of the American Mathematical Society 80 Discrete and Continuous Dynamical Systems 71 Journal of Differential Equations 66 Journal of Functional Analysis 63 Journal of Fluid Mechanics 60 Inventiones Mathematicae 56 Journal of Mathematical Analysis and Applications 52 Nonlinearity 51 Israel Journal of Mathematics 50 Proceedings of the American Mathematical Society 49 Advances in Mathematics 43 Annales Henri Poincaré 39 The Annals of Probability 39 Probability Theory and Related Fields 39 Dynamical Systems 38 Reviews in Mathematical Physics 38 Journal of Dynamics and Differential Equations 33 Nonlinear Dynamics 30 Reports on Mathematical Physics 29 Letters in Mathematical Physics 28 Journal of Mathematical Biology 28 Applied Mathematics and Computation 28 Mathematische Zeitschrift 27 Archive for Rational Mechanics and Analysis 27 Stochastics and Dynamics 26 Stochastic Processes and their Applications 25 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 25 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 25 Bulletin of the American Mathematical Society. New Series 24 Physics Letters. A 24 Annales de l’Institut Henri Poincaré. Physique Théorique 24 Communications in Nonlinear Science and Numerical Simulation 23 Journal of Nonlinear Science 21 Mathematische Annalen 21 Monatshefte für Mathematik 20 Journal of Computational Physics 20 Duke Mathematical Journal 20 Physics of Fluids 18 Physica A 18 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 17 Theoretical and Mathematical Physics 17 Publications Mathématiques 17 The Annals of Applied Probability 17 Journal of Difference Equations and Applications 17 Journal of Statistical Mechanics: Theory and Experiment 16 International Journal of Modern Physics B 16 Bulletin of Mathematical Biology 15 International Journal of Theoretical Physics 15 Journal of the European Mathematical Society (JEMS) 15 Acta Mathematica Sinica. English Series 15 Nonlinear Analysis. Theory, Methods & Applications 14 Mathematical Proceedings of the Cambridge Philosophical Society 14 Physics Reports 14 Acta Mathematica 14 Annales de l’Institut Fourier 14 Physical Review Letters 14 Discrete and Continuous Dynamical Systems. Series B 14 Journal of Modern Dynamics 13 Journal d’Analyse Mathématique 13 Annals of Physics 13 Qualitative Theory of Dynamical Systems 12 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section A. Physique Théorique 12 Mathematical Problems in Engineering 11 Geometriae Dedicata 11 Journal of Economic Theory 11 Mathematische Nachrichten 11 Entropy 11 SIAM Journal on Applied Dynamical Systems 11 Science China. Mathematics 10 Modern Physics Letters B 10 The Mathematical Intelligencer 10 Functional Analysis and its Applications 10 Mathematical and Computer Modelling 10 Infinite Dimensional Analysis, Quantum Probability and Related Topics 10 Journal of High Energy Physics 10 Bulletin of the Brazilian Mathematical Society. New Series 10 Foundations of Physics 10 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 9 Ukrainian Mathematical Journal 9 Physics of Fluids, A 9 The Annals of Statistics 9 Memoirs of the American Mathematical Society 9 Advances in Applied Mathematics 9 Dynamics and Stability of Systems 8 Advances in Applied Probability 8 Biological Cybernetics 8 Lithuanian Mathematical Journal 8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 8 Synthese 8 Theoretical Population Biology 8 Geometric and Functional Analysis. GAFA 8 Indagationes Mathematicae. New Series ...and 403 more Serials
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### Cited in 62 Fields

 2,627 Dynamical systems and ergodic theory (37-XX) 1,189 Statistical mechanics, structure of matter (82-XX) 854 Probability theory and stochastic processes (60-XX) 404 Ordinary differential equations (34-XX) 365 Fluid mechanics (76-XX) 346 Measure and integration (28-XX) 331 Quantum theory (81-XX) 283 Partial differential equations (35-XX) 273 Functional analysis (46-XX) 221 Biology and other natural sciences (92-XX) 181 Operator theory (47-XX) 166 Global analysis, analysis on manifolds (58-XX) 145 Statistics (62-XX) 136 Information and communication theory, circuits (94-XX) 134 Numerical analysis (65-XX) 120 Differential geometry (53-XX) 108 Number theory (11-XX) 107 Mechanics of particles and systems (70-XX) 105 Functions of a complex variable (30-XX) 105 General topology (54-XX) 88 Systems theory; control (93-XX) 84 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 75 Computer science (68-XX) 67 Manifolds and cell complexes (57-XX) 63 Combinatorics (05-XX) 55 Classical thermodynamics, heat transfer (80-XX) 54 Difference and functional equations (39-XX) 51 Several complex variables and analytic spaces (32-XX) 51 Geophysics (86-XX) 43 Linear and multilinear algebra; matrix theory (15-XX) 41 Topological groups, Lie groups (22-XX) 40 Real functions (26-XX) 39 Harmonic analysis on Euclidean spaces (42-XX) 34 Mechanics of deformable solids (74-XX) 31 General and overarching topics; collections (00-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 27 Group theory and generalizations (20-XX) 24 History and biography (01-XX) 22 Mathematical logic and foundations (03-XX) 22 Operations research, mathematical programming (90-XX) 21 Relativity and gravitational theory (83-XX) 20 Convex and discrete geometry (52-XX) 19 Approximations and expansions (41-XX) 18 Algebraic topology (55-XX) 18 Optics, electromagnetic theory (78-XX) 15 Potential theory (31-XX) 15 Integral equations (45-XX) 13 Algebraic geometry (14-XX) 13 Abstract harmonic analysis (43-XX) 9 Astronomy and astrophysics (85-XX) 7 Nonassociative rings and algebras (17-XX) 7 $$K$$-theory (19-XX) 6 Special functions (33-XX) 4 Integral transforms, operational calculus (44-XX) 3 Commutative algebra (13-XX) 3 Category theory; homological algebra (18-XX) 3 Sequences, series, summability (40-XX) 3 Geometry (51-XX) 3 Mathematics education (97-XX) 2 Field theory and polynomials (12-XX) 2 Associative rings and algebras (16-XX) 1 Order, lattices, ordered algebraic structures (06-XX)

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