One-parameter families of smooth interval maps: Density of hyperbolicity and robust chaos

DOI10.1090/S0002-9939-2010-10446-XzbMath1230.37049arXiv0912.0656OpenAlexW2031822029MaRDI QIDQ3065724

Sebastian J. van Strien

Publication date: 6 January 2011

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

Full work available at URL: https://arxiv.org/abs/0912.0656

zbMATH Keywords

periodic attractorrobust chaosunimodal family of maps

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Dynamical systems involving maps of the interval (37E05) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

Related Items (5)

Positive transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps ⋮ A constructive approach to robust chaos using invariant manifolds and expanding cones ⋮ Hidden dynamics for piecewise smooth maps ⋮ Monotonicity of entropy for real multimodal maps ⋮ Density of hyperbolicity for classes of real transcendental entire functions and circle maps

Cites Work

• Unnamed Item
• Robust chaos with variable Lyapunov exponent in smooth one-dimensional maps
• One-dimensional dynamics in the new millennium
• Bifurcations and stability of families of diffeomorphisms
• A structure theorem in one dimensional dynamics
• Density of hyperbolicity for classes of real transcendental entire functions and circle maps
• Rigidity for real polynomials
• Density of hyperbolicity in dimension one
• Real bounds, ergodicity and negative Schwarzian for multimodal maps
• Robust Chaos

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