Geometric Lorenz flows with historic behavior

DOI10.3934/dcds.2016105zbMath1368.37026arXiv1511.05257OpenAlexW3106492309MaRDI QIDQ727422

Ming-Chia Li, Teruhiko Soma, Shin Kiriki

Publication date: 6 December 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.05257

zbMATH Keywords

Lorenz mapgeometric Lorenz flowhistoric behavior

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Dynamics induced by flows and semiflows (37C10) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Partially hyperbolic systems and dominated splittings (37D30) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (16)

Emergence via non-existence of averages ⋮ Irregular sets for piecewise monotonic maps ⋮ Historic behavior in discrete-time replicator dynamics ⋮ Abundance of wild historic behavior ⋮ Stable and historic behavior in replicator equations generated by similar-order preserving mappings ⋮ Persistent non-statistical dynamics in one-dimensional maps ⋮ Historic behavior in rock-paper-scissor dynamics ⋮ Historic behavior in nonautonomous rock-paper-scissors dynamics ⋮ Uniformly historic behaviour in compact dynamical systems ⋮ Unnamed Item ⋮ Complete set of invariants for a Bykov attractor ⋮ Historic behavior in nonhyperbolic homoclinic classes ⋮ On the historical behavior of singular hyperbolic attractors ⋮ The dynamics of vector fields with singularities ⋮ Historic behaviour vs. physical measures for irrational flows with multiple stopping points ⋮ Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems

Uses Software

• RODES

Cites Work

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• Takens' last problem and existence of non-trivial wandering domains
• Structural stability of Lorenz attractors
• The structure of Lorenz attractors
• A rigorous ODE solver and Smale's 14th problem
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Historic behaviour for random expanding maps on the circle
• The mean and transitive points of homeomorphisms
• Singular-hyperbolic attractors are chaotic
• Higher order Birkhoff averages
• Singular hyperbolic systems
• Heteroclinic attractors: Time averages and moduli of topological conjugacy
• Deterministic Nonperiodic Flow
• On Takens’ last problem: tangencies and time averages near heteroclinic networks
• Orbits with historic behaviour, or non-existence of averages

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