Limit sets of S-unimodal maps with zero entropy

DOI10.1007/BF01205554zbMath0625.58027MaRDI QIDQ579702

John Guckenheimer

Publication date: 1987

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

zbMATH Keywords

period doublingnonwandering setrenormalization theory of FeigenbaumSchwarzian negative

Mathematics Subject Classification ID

Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (16)

Measurable dynamics of $S$-unimodal maps of the interval ⋮ Measure and dimension of solenoidal attractors of one-dimensional dynamical systems ⋮ Markov partitions and Feigenbaum-like mappings ⋮ Dynamics of quadratic polynomials: complex bounds for real maps ⋮ Backward Asymptotics in S-Unimodal Maps ⋮ Distortion results and invariant Cantor sets of unimodal maps ⋮ Critical circle maps near bifurcation ⋮ Metric properties of non-renormalizable S-unimodal maps: II. Quasisymmetric conjugacy classes ⋮ Hyperbolicity and invariant measures for general \(C^ 2\) interval maps satisfying the Misiurewicz condition ⋮ Ergodic properties of transformations of an interval ⋮ Measure of minimal sets of polymodal maps ⋮ Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems: 1. The case of negative Schwarzian derivative ⋮ Julia-Fatou-Sullivan theory for real one-dimensional dynamics ⋮ The Fibonacci Unimodal Map ⋮ Measure of solenoidal attractors of unimodal maps of the segment ⋮ Induced expansion for quadratic polynomials

Cites Work

• Sensitive dependence to initial conditions for one dimensional maps
• Stable Orbits and Bifurcation of Maps of the Interval

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