Markov extensions, zeta functions, and Fredholm theory for piecewise invertible dynamical systems

1989/02/01 by G. Keller, Gerhard Keller · 7 citations
Mathematics · Physics and Astronomy · Computer Science · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Nonlinear Dynamics and Pattern Formation

paper · doi:10.1090/s0002-9947-1989-1005524-4

Abstract

Abstract. Transfer operators and zeta functions of piecewise monotonie and of more general piecewise invertible dynamical systems are studied. To this end we construct Markov extensions of given systems, develop a kind of Fredholm theory for them, and carry the results back to the original systems. This yields e.g. bounds on the number of ergodic maximal measures or equilibrium states. 1.

Cited by

• Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties
• Symbolic dynamics for surface diffeomorphisms with positive topological\n entropy
• Spectral gap of sparse bistochastic matrices with exchangeable rows with application to shuffle-and-fold maps
• Subshifts and C*-algebras from one-counter codes
• Dimension groups for interval maps
• Computation of Topological Entropy via ϕ-expansion, an Inverse Problem for the Dynamical Systems βx+α\mod 1
• A Proof of the Conjecture of Lehmer and of the Conjecture of Schinzel-Zassenhaus

Related

• Thermodynamic formalism for some systems with countable Markov structures
• Some Probabilistic Properties of General Topological Markov Chains
• Convergence of pushforward measures for certain countably piecewise linear Markov maps
• Finitely presented dynamical systems
• Some simple but challenging Markov processes