Topological pressure via saddle points

DOI10.1090/S0002-9947-07-04407-8zbMath1124.37020arXivmath/0509630OpenAlexW1989139665MaRDI QIDQ5423919

Katrin Gelfert, Christian Wolf

Publication date: 1 November 2007

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0509630

zbMATH Keywords

invariant measuresHausdorff dimensionsaddle pointstopological pressure\(C^2\)-diffeomorphism

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dimension theory of smooth dynamical systems (37C45)

Related Items (10)

Topological pressure dimension ⋮ Dynamical quantities and their numerical analysis by saddle periodic orbits ⋮ The growth of periodic orbits with large support ⋮ On the approximation of dynamical indicators in systems with nonuniformly hyperbolic behavior ⋮ Geometry and entropy of generalized rotation sets ⋮ Topological pressure for nonautonomous systems ⋮ Equality of pressures for diffeomorphisms preserving hyperbolic measures ⋮ On the commutativity of coset pressure ⋮ On the weaker forms of the specification property and their applications ⋮ Horseshoes for \(\mathcal{C}^{1+\alpha}\) mappings with hyperbolic measures

Cites Work

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• The ergodic theory of axiom A flows
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• Topological entropy and periodic orbits of saddle type for surface diffeomorphisms
• Stable sets, hyperbolicity and dimension
• Abnormal escape rates from nonuniformly hyperbolic sets
• Expanding Periodic Orbits with Small Exponents
• A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems
• Some Large Deviation Results for Dynamical Systems
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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