Continuity of the Hausdorff dimension for piecewise monotonic maps

DOI10.1007/BF02808156zbMath0768.28010MaRDI QIDQ1802777

Peter Raith

Publication date: 29 June 1993

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

perturbationstopological pressurepiecewise monotonic mapHausdorff dimension function

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Hausdorff and packing measures (28A78) One-parameter continuous families of measure-preserving transformations (28D10)

Related Items (11)

Unnamed Item ⋮ The space of ω-limit sets of piecewise continuous maps of the interval ⋮ Stability of the distribution function for piecewise monotonic maps on the interval ⋮ The bifurcation locus for numbers of bounded type ⋮ Entropy formula and continuity of entropy for piecewise expanding maps ⋮ Mixing properties in expanding Lorenz maps ⋮ Continuity of the measure of maximal entropy for unimodal maps on the interval ⋮ The -transformation with a hole at 0 ⋮ Matching for generalised \(\beta\)-transformations ⋮ Topological transitivity for a class of monotonic mod one transformations ⋮ Stability of the topological pressure for piecewise monotonic maps under \(C^1\)-perturbations

Cites Work

• Piecewise invertible dynamical systems
• Topologically transitive subsets of piecewise monotonic maps, which contain no periodic points
• Jumps of entropy in one dimension
• Invariant subsets of expanding mappings of the circle
• Entropy of piecewise monotone mappings
• Hausdorff dimension for piecewise monotonic maps
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Unnamed Item

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