Nonuniformly expanding 1D maps

DOI10.1007/s00220-005-1485-4zbMath1107.37028OpenAlexW2115726772MaRDI QIDQ852407

Qiudong Wang, Lai-Sang Young

Publication date: 29 November 2006

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-005-1485-4

zbMATH Keywords

invariant measure1-parameter families of 1D mapsexpanding propertynonuniform expansion

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Dynamical systems involving maps of the circle (37E10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical systems involving maps of the interval (37E05)

Related Items (14)

Large strange attractors in the unfolding of a heteroclinic attractor ⋮ Dirac physical measures on saddle-type fixed points ⋮ Positive Lyapunov exponent by a random perturbation ⋮ Dynamics of homoclinic tangles in periodically perturbed second-order equations ⋮ Positive Lyapunov exponent for random perturbations of predominantly expanding multimodal circle maps ⋮ Large deviations in non-uniformly hyperbolic dynamical systems ⋮ Lyapunov exponents for random perturbations of some area-preserving maps including the standard map ⋮ Functional norms for Young towers ⋮ Structure and \(f\)-dependence of the a.c.i.m. for a unimodal map \(f\) of Misiurewicz type ⋮ Absolutely continuous invariant measure of a map from grazing-impact oscillators ⋮ Dissipative homoclinic loops of two-dimensional maps and strange attractors with one direction of instability ⋮ Strange Attractors for Periodically Forced Parabolic Equations ⋮ Dynamical profile of a class of rank-one attractors ⋮ Rank-one strange attractors \textit{versus} heteroclinic tangles

Cites Work

• The dynamics of the Hénon map
• On iterations of \(1-\alpha x^2\) on \((-1,1)\)
• Absolutely continuous measures for certain maps of an interval
• Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
• A proof of Benedicks-Carleson-Jacobson theorem
• Positive Lyapunov exponent for generic one-parameter families of unimodal maps
• From invariant curves to strange attractors
• Invariant measures exist under a summability condition for unimodal maps
• Toward a theory of rank one attractors
• Positive Liapunov exponents and absolute continuity for maps of the interval
• Absolutely continuous invariant measures and random perturbations for certain one-dimensional maps
• Strange attractors with one direction of instability

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