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Ergodic theory of chaos and strange attractors
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
A new graphical tool for measuring the time constancy of dynamical systems is presented and illustrated with typical examples.
Statistical Mechanics: Rigorous Results
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
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
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
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
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
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
Thermodynamic Formalism: The Mathematical Structures of Classical Equilibrium Statistical Mechanics
This book is aimed at mathematicians interested in such topics as ergodic theory, topological dynamics, constructive quantum field theory, the study of certain differentiable dynamical systems,
Ergodic theory of differentiable dynamical systems
Iff is a C1 + ɛ diffeomorphism of a compact manifold M, we prove the existence of stable manifolds, almost everywhere with respect to everyf-invariant probability measure on M. These stable manifolds