Positive Lyapunov exponent for generic one-parameter families of unimodal maps
From MaRDI portal
Publication:1343309
DOI10.1007/BF03008407zbMath0821.58015OpenAlexW2022715085MaRDI QIDQ1343309
Charles Tresser, Philippe Thieullen, Lai-Sang Young
Publication date: 19 September 1995
Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf03008407
Ergodic theory (37A99) Low-dimensional dynamical systems (37E99) One-parameter continuous families of measure-preserving transformations (28D10)
Related Items
Random perturbations and statistical properties of Hénon-like maps, Nonuniformly expanding 1D maps, Summability implies Collet–Eckmann almost surely, Expansion properties of double standard maps, On the abundance of chaotic behavior for generic one-parameter families of maps, RANK ONE CHAOS: THEORY AND APPLICATIONS, Destabilization and chaos induced by harvesting: insights from one-dimensional discrete-time models, From limit cycles to strange attractors, Topological and metrical conditions for Collet-Eckmann unimodal maps, Abundance of non-uniform hyperbolicity in bifurcations of surface endomorphisms, Strange attractors in periodically-kicked degenerate Hopf bifurcations, Dissipative homoclinic loops of two-dimensional maps and strange attractors with one direction of instability, Dynamical profile of a class of rank-one attractors, How does noise induce order?
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The dynamics of the Hénon map
- Hyperbolicity and invariant measures for general \(C^ 2\) interval maps satisfying the Misiurewicz condition
- On iterations of \(1-\alpha x^2\) on \((-1,1)\)
- Erratum. Hyperbolicity, sinks and measure in one dimensional dynamics
- Absolutely continuous invariant measures for \(C^ 2\) unimodal maps satisfying the Collet-Eckmann conditions
- Sensitive dependence to initial conditions for one dimensional maps
- Absolutely continuous measures for certain maps of an interval
- Absolutely continuous invariant measures for one-parameter families of one-dimensional maps
- Julia-Fatou-Sullivan theory for real one-dimensional dynamics
- Positive Lyapunov exponents in families of one dimensional dynamical systems
- Invariant measures exist under a summability condition for unimodal maps
- Positive Liapunov exponents and absolute continuity for maps of the interval
- Positive measure sets of ergodic rational maps
- A positive Liapunov exponent for the critical value of an S-unimodal mapping implies uniform hyperbolicity
- Another proof of Jakobson's Theorem and related results
- Stable Orbits and Bifurcation of Maps of the Interval