Almost complete Lyapunov spectrum in step skew-products

DOI10.1080/14689367.2012.753992zbMath1347.37059OpenAlexW1981026895MaRDI QIDQ5298831

Michał Rams, Katrin Gelfert, Lorenzo J. Dıaz

Publication date: 24 June 2013

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689367.2012.753992

zbMATH Keywords

Lyapunov exponentsspectral gapminimalitypartial hyperbolicityhomoclinic classnon-contracting iterated function systems

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Partially hyperbolic systems and dominated splittings (37D30)

Related Items

Generation of spines in porcupine-like horseshoes, Non-hyperbolic iterated function systems: semifractals and the chaos game, Invariant multi-graphs in step skew-products, The structure of the space of ergodic measures of transitive partially hyperbolic sets, Porcupine-Like Horseshoes: Topological and Ergodic Aspects

Cites Work

• On the Hausdorff dimension of invariant measures of weakly contracting on average measurable IFS
• Contracting on average random IFS with repelling fixed point
• Nonremovable zero Lyapunov exponent
• Porcupine-like horseshoes: Transitivity, Lyapunov spectrum, and phase transitions
• Rich phase transitions in step skew products
• Dimension theory of iterated function systems
• Non-hyperbolic ergodic measures with large support
• Destroying horseshoes via heterodimensional cycles: generating bifurcations inside homoclinic classes