Dimension estimates in smooth dynamics: a survey of recent results
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Publication:3012875
DOI10.1017/S014338571000012XzbMath1230.37032OpenAlexW2127075618MaRDI QIDQ3012875
Publication date: 7 July 2011
Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s014338571000012x
Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dimension theory of smooth dynamical systems (37C45)
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Cites Work
- Unnamed Item
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- Number theoretical peculiarities in the dimension theory of dynamical systems.
- Local estimates for the Hausdorff dimension of an attractor
- Multifractal analysis for Lyapunov exponents on nonconformal repellers
- Some relations between dimension and Lyapunov exponents
- Infinite-dimensional dynamical systems in mechanics and physics
- Negatively invariant sets of compact maps and an extension of a theorem of Cartwright
- Hölder continuity for the inverse of Mañé's projection
- Box dimensions and topological pressure for some expanding maps
- Measures of maximal dimension for hyperbolic diffeomorphisms
- Maximum local Lyapunov dimension bounds the box dimension. Direct proof for invariant sets on Riemannian manifolds
- SRB measures for Axiom A endomorphisms
- Expansiveness, hyperbolicity and Hausdorff dimension
- The dimensions of some self-affine limit sets in the plane and hyperbolic sets
- Hausdorff dimension estimates for invariant sets of time-dependent vector fields
- The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
- Ergodic theory of parabolic horseshoes
- Hausdorff dimension for non-hyperbolic repellers. II: DA diffeomorphisms
- Fractal dimensions for repellers of maps with holes
- Local and global Lyapunov exponents
- Measure of full dimension for some nonconformal repellers
- The box dimension of self-affine graphs and repellers
- The Hausdorff dimension of the Smale-Williams solenoid with different contraction coefficients
- Invariant measures of full dimension for some expanding maps
- Hausdorff dimension for non-invertible maps
- An upper estimate of the Hausdorff dimension of stable sets
- The Hausdorff dimension of horseshoes of diffeomorphisms of surfaces
- Hausdorff dimension for horseshoes
- The Hausdorff dimension of general Sierpiński carpets
- Hausdorff dimension for an open class of repellers in
- Dimensions of compact invariant sets of some expanding maps
- Dimension, entropy and Lyapunov exponents
- The Hausdorff dimension of self-affine fractals
- A subadditive thermodynamic formalism for mixing repellers
- Discontinuity of Hausdorff dimension and limit capacity on arcs of diffeomorphisms
- Hausdorff dimension for horseshoes in $\mathbb{R}^3$
- An upper bound for the Hausdorff dimension of a hyperbolic set
- The dimension of self-affine fractals II
- Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
- A Variational Principle for the Pressure of Continuous Transformations
- Hausdorff dimension estimates for invariant sets with an equivariant tangent bundle splitting
- Measure and dimension for some fractal families
- Bounded distortion and dimension for non-conformal repellers
- Regularity of the Anosov splitting and of horospheric foliations
- The self-affine carpets of McMullen and Bedford have infinite Hausdorff measure
- Falconer's formula for the Hausdorff dimension of a self-affine set in R2
- Dynamical upper bounds for Hausdorff dimension of invariant sets
- Finite fractal dimension and Holder-Lipshitz parametrization
- Maximum local Lyapunov dimension bounds the box dimension of chaotic attractors
- Statistical Mechanics on a Compact Set with Z p Action Satisfying Expansiveness and Specification
- Dimension estimates in nonconformal hyperbolic dynamics*
- Dimension product structure of hyperbolic sets
- Measures and dimensions in conformal dynamics
- A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems
- Regularity of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces
- Repellers for real analytic maps
- On measures of maximal and full dimension for polynomial automorphisms of ℂ²
- The Hausdorff dimension of certain solenoids
- Measures of full dimension on affine-invariant sets
- The box and Hausdorff dimension of self-affine sets
- Subadditive pressure for triangular maps
- Dimension estimates beyond conformal and hyperbolic dynamics
- A variational principle for the dimension for a class of non-conformal repellers
- Asymptotic Hausdorff dimensions of Cantor sets associated with an asymptotically non-hyperbolic family
- Equilibrium states and the ergodic theory of Anosov diffeomorphisms
- A note on the fractal dimension of attractors of dissipative dynamical systems
- Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes
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