On the rotation sets of generic homeomorphisms on the torus

DOI10.1017/etds.2020.92zbMath1479.37040arXiv1901.00396OpenAlexW3092308522WikidataQ114119072 ScholiaQ114119072MaRDI QIDQ4958307

Heides Lima, Paulo Varandas

Publication date: 7 September 2021

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.00396

zbMATH Keywords

topological entropyspecificationrotation setsmetric mean dimensiongluing orbit propertyhistoric behaviorhomeomorphisms on tori

Mathematics Subject Classification ID

Topological entropy (37B40) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Rotation numbers and vectors (37E45)

Related Items (10)

Entropy of irregular points for some dynamical systems ⋮ Sensitivity and historic behavior for continuous maps on Baire metric spaces ⋮ Rotational entropy -- a homotopy invariant for torus maps ⋮ Rotation sets and rotational entropy for random dynamical systems on the torus ⋮ Realization of rotation vectors for volume preserving homeomorphisms of the torus ⋮ On the structure of rotation sets in hyperbolic surfaces ⋮ The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows ⋮ Unnamed Item ⋮ Generic homeomorphisms have full metric mean dimension ⋮ Entropy spectrum of rotation classes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topological features of flows with the reparametrized gluing orbit property
• Bifurcations and stability of families of diffeomorphisms
• Topological pressure and the variational principle for noncompact sets
• A remark on the topological entropy of homeomorphisms
• Ergodic theory on compact spaces
• On the periodic orbits, shadowing and strong transitivity of continuous flows
• The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows
• Shadowing is generic
• A multifractal formalism
• Mean topological dimension
• Topological invariants of dynamical systems and spaces of holomorphic maps. I.
• Sets of ``non-typical points have full topological entropy and full Hausdorff dimension
• Geometry and entropy of generalized rotation sets
• The rotation sets of most volume preserving homeomorphisms on \(\mathbb{T}^d\) are stable, convex and rational polyhedrons
• Gluing orbit property and partial hyperbolicity
• Irregular sets are residual
• Minimality and gluing orbit property
• Curves von 2-manifolds and isotopies
• Generic properties of invariant measures for Axiom A diffeomorphisms
• Rotation, entropy, and equilibrium states
• Variational principles and mixed multifractal spectra
• A priori degeneracy of one-dimensional rotation sets for periodic point free torus maps
• Points with maximal Birkhoff average oscillation
• On the genericity of the shadowing property for conservative homeomorphisms
• On the irregular points for systems with the shadowing property
• Entropy and rotation sets: A toy model approach
• Diffeomorphisms having rotation sets with non-empty interior
• Rotation Sets of Toral Flows
• The irregular set for maps with the specification property has full topological pressure
• Rotation Sets for Maps of Tori
• Realizing Rotation Vectors for Torus Homeomorphisms
• A Minimal Positive Entropy Homeomorphism of the 2-Torus
• Rotation sets and ergodic measures for torus homeomorphisms
• Every convex polygon with rational vertices is a rotation set
• Dynamics of topologically generic homeomorphisms
• On the variational principle for the topological entropy of certain non-compact sets
• NORMAL AND NON-NORMAL POINTS OF SELF-SIMILAR SETS AND DIVERGENCE POINTS OF SELF-SIMILAR MEASURES
• The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples
• Area-preserving diffeomorphisms of the torus whose rotation sets have non-empty interior
• Multifractal analysis for the historic set in topological dynamical systems
• Stability of the rotation set of area-preserving toral homeomorphisms
• From Rate Distortion Theory to Metric Mean Dimension: Variational Principle
• Rational polygons as rotation sets of generic homeomorphisms of the two torus
• Orbits with historic behaviour, or non-existence of averages
• Differentiable dynamical systems
• Entropy for Group Endomorphisms and Homogeneous Spaces
• Topological entropy for divergence points

This page was built for publication: On the rotation sets of generic homeomorphisms on the torus