Ergodic theory of chaos and strange attractors
- J. Eckmann, D. Ruelle
- Physics
- 1 July 1985
Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the…
Recurrence Plots of Dynamical Systems
- J. Eckmann, S. O. Kamphorst, D. Ruelle
- Physics
- 1 November 1987
A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples.
Statistical Mechanics: Rigorous Results
- D. Ruelle
- Physics
- 14 April 1999
Thermodynamic behaviour - ensembles the thermodynamic limit for thermodynamic functions - lattice systems the thermodynamic limit for thermodynamic functions - continuous systems low density…
Superstable interactions in classical statistical mechanics
- D. Ruelle
- Mathematics
- 1970
AbstractWe consider classical systems of particles inv dimensions. For a very large class of pair potentials (superstable lower regular potentials) it is shown that the correlation functions have…
On the nature of turbulence
A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed.
Zeta-functions for expanding maps and Anosov flows
- D. Ruelle
- Mathematics
- 1 October 1976
Given a real-analytic expanding endomorphism of a compact manifoldM, a meromorphic zeta function is defined on the complex-valued real-analytic functions onM. A zeta function for Anosov flows is…
Repellers for real analytic maps
- D. Ruelle
- MathematicsErgodic Theory and Dynamical Systems
- 1 March 1982
Abstract The purpose of this note is to prove a conjecture of D. Sullivan that when the Julia set J of a rational function f is hyperbolic, the Hausdorff dimension of J depends real analytically on…
A MEASURE ASSOCIATED WITH AXIOM-A ATTRACTORS.
- D. Ruelle
- Mathematics
- 23 January 1976
The future orbits of a diffeomorphism near an Axiom-A attrac- tor are investigated. It is found that their asymptotic behavior is in general described by a fixed probability measure yt carried by the…
The Ergodic Theory of Axiom A Flows.
Let M be a compact (Riemann) manifold and (f t ): M → M a differentiable flow. A closed (f t )-invariant set ∧ ⊂ M containing no fixed points is hyperbolic if the tangent bundle restricted to ∧ can…
Differentiation of SRB States
- D. Ruelle
- Mathematics
- 1 July 1997
Dedicated to Klaus Hepp and Walter Hunziker for their 60th birthdays.Abstract:Let f be a diffeomorphism of a manifold M, and ρf a (generalized) SRB state for f. If supp ρf is a hyperbolic compact set…
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