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Variational principles for nonautonomous dynamical systems

Andrzej Biś

Abstract

We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure functions determined by the system.

Variational principles for nonautonomous dynamical systems

Abstract

We study thermodynamical formalism of a discrete nonautonomous dynamical system determined by a sequence of continuous self-maps of a compact metric space. Using the methods of Convex Analysis we get variational principles for pressure functions determined by the system.
Paper Structure (14 sections, 9 theorems, 83 equations)

This paper contains 14 sections, 9 theorems, 83 equations.

Table of Contents

  1. Introduction and structure of the paper
  2. Main results
  3. Abstract variational principle
  4. Topological entropy and topological pressure of NADDS
  5. Basic definitions and properties
  6. Proof of Theorem A
  7. Proof of Corollary 1
  8. Proof of Theorem B
  9. Misiurewicz entropy and Misiurewicz pressure for NADDS
  10. Basic definitions
  11. Pressure function
  12. Proof of Theorem C
  13. Proof of Corollary 2
  14. Proof of Theorem D

Key Result

Theorem 3.2

BCMV Let $(X,d)$ be a metric space and $\Gamma: {\mathbf B} \to \mathbb{R}$ be a pressure function.

Theorems & Definitions (29)

  • Example 2.1
  • Example 2.2
  • Remark 2.3
  • Definition 3.1
  • Theorem 3.2
  • Definition 4.1
  • Lemma 4.2
  • proof
  • Lemma 4.3
  • proof
  • ...and 19 more