Complete spectral data for analytic Anosov maps of the torus

DOI10.1088/1361-6544/aa700fzbMath1379.37068arXiv1605.02883OpenAlexW2375764343MaRDI QIDQ4978480

Wolfram Just, Oscar F. Bandtlow, Julia Slipantschuk

Publication date: 11 August 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.02883

zbMATH Keywords

transfer operatorAnosov diffeomorphismcorrelation spectrumBlaschke map

Mathematics Subject Classification ID

Ergodic theory of linear operators (47A35) Ergodicity, mixing, rates of mixing (37A25) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Related Items (12)

The work of Sébastien Gouëzel on limit theorems and on weighted Banach spaces ⋮ Explicit examples of resonances for Anosov maps of the torus ⋮ Dynamics of low-degree rational inner skew-products on $\mathbb{T}^2$ ⋮ Generic non-trivial resonances for Anosov diffeomorphisms ⋮ Dynamic mode decomposition for analytic maps ⋮ Sinai billiard maps with Ruelle resonances ⋮ Linear encoding of the spatiotemporal cat ⋮ Transfer operators for ultradifferentiable expanding maps of the circle ⋮ Ruelle spectrum of linear pseudo-Anosov maps ⋮ Parabolic dynamics and anisotropic Banach spaces ⋮ On the rate of mixing of circle extensions of Anosov maps ⋮ Locating Ruelle–Pollicott resonances*

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Band structure of the Ruelle spectrum of contact Anosov flows
• The Ruelle spectrum of generic transfer operators
• Spectral structure of transfer operators for expanding circle maps
• The quest for the ultimate anisotropic Banach space
• Generalized spectral decomposition of the \(\beta\)-adic baker's transformation and intrinsic irreversibility
• Non-diagonalizability of the Frobenius-Perron operator and transition between decay modes of the time autocorrelation function.
• Spectral decomposition of piecewise linear monotonic maps.
• Resolvent estimates for operators belonging to exponential classes
• Compact locally maximal hyperbolic sets for smooth maps: Fine statistical properties
• Banach spaces for piecewise cone-hyperbolic maps
• On the rate of mixing of Axiom A flows
• Meromorphic extensions of generalised zeta functions
• Locating resonances for axiom A dynamical systems
• Jordan blocks in a one-dimensional Markov map
• Invariant distributions and time averages for horocycle flows
• Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms
• Explicit eigenvalue estimates for transfer operators acting on spaces of holomorphic functions
• On a theorem of Anosov
• Time-Correlation Functions of One-Dimensional Transformations
• Dimension theoretical properties of generalized Baker's transformations
• Banach spaces adapted to Anosov systems
• On the Ruelle eigenvalue sequence
• On Finite Blaschke Products whose Restrictions to the unit circle are Exact Endomorphisms
• The correlation spectrum for hyperbolic analytic maps
• Chaotic dynamics, fluctuations, nonequilibrium ensembles
• Lower bounds for the Ruelle spectrum of analytic expanding circle maps
• Ruelle Perron Frobenius spectrum for Anosov maps
• On the discrete time version of the Brussels formalism
• On the relation between Lyapunov exponents and exponential decay of correlations
• Generic non-trivial resonances for Anosov diffeomorphisms
• Dynamics of two-dimensional Blaschke products
• Analytic expanding circle maps with explicit spectra
• Ruelle–Pollicott resonances for real analytic hyperbolic maps

This page was built for publication: Complete spectral data for analytic Anosov maps of the torus