On Hausdorff dimension of unimodal attractors

DOI10.1007/s00220-006-1540-9zbMath1114.37021OpenAlexW1966043371MaRDI QIDQ865066

Jacek Graczyk, O. S. Kozlovski

Publication date: 13 February 2007

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

Full work available at URL: https://doi.org/10.1007/s00220-006-1540-9

zbMATH Keywords

Schwarzian derivativecritical pointHausdorff dimensionattractorcross-ratiounimodal map

Mathematics Subject Classification ID

Stability of topological dynamical systems (37B25) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Dynamical systems involving maps of the interval (37E05) Universality and renormalization of dynamical systems (37E20) Dimension theory of smooth dynamical systems (37C45)

Related Items (2)

\(\alpha\)-limit sets and Lyapunov function for maps with one topological attractor ⋮ Hausdorff dimension of Cantor attractors in one-dimensional dynamics

Cites Work

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• Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups
• On the concept of attractor
• On the bass note of a Schottky group
• Non-uniform hyperbolicity and universal bounds for \(S\)-unimodal maps
• Julia-Fatou-Sullivan theory for real one-dimensional dynamics
• The limit set of a Fuchsian group
• Quantitative universality for a class of nonlinear transformations
• Combinatorics, geometry and attractors of quasi-quadratic maps
• Metric attractors for smooth unimodal maps
• Wild Cantor attractors exist
• Critical circle maps near bifurcation
• Decay of geometry for unimodal maps: Negative Schwarzian case
• The Real Fatou Conjecture
• Metric properties of non-renormalizableS-unimodal maps. Part I: Induced expansion and invariant measures
• Induced expansion for quadratic polynomials
• Getting rid of the negative Schwarzian derivative condition

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