Markov Extensions, Zeta Functions, and Fredholm Theory for Piecewise Invertible Dynamical Systems

DOI10.2307/2001395zbMath0686.58027OpenAlexW4230470648MaRDI QIDQ4204846

Gerhard Keller

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001395

zbMATH Keywords

equilibrium stateszeta functionstransfer operatorsFredholm theoryMarkov extensionspiecewise invertible dynamical systemsergodic maximal measuresmonotonic dynamical systems

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)

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The Pianigiani-Yorke measure for topological Markov chains, Exponents, attractors and Hopf decompositions for interval maps, Unnamed Item, Discontinuities cause essential spectrum, Dynamic mode decomposition for analytic maps, Lifting measures to Markov extensions, Large deviations in non-uniformly hyperbolic dynamical systems, On the essential spectrum of the transfer operator for expanding Markov maps, Limiting distributions for countable state topological Markov chains with holes, Existence and convergence properties of physical measures for certain dynamical systems with holes, Spectral theory, zeta functions and the distribution of periodic points for Collet-Eckmann maps, Symbolic dynamics for surface diffeomorphisms with positive entropy, On the dimension of the space of harmonic functions on transitive shift spaces, Markov extensions for multi-dimensional dynamical systems, Exponential mixing for skew products with discontinuities, On the Fredholm determination of a piecewise linear transformation, Ergodicité intrinsèque de produits fibrés d'applications chaotiques unidimensionnelles, Decay of correlations for piecewise invertible maps in higher dimensions

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