Shrinking targets in parametrised families

DOI10.1017/S0305004117000822zbMath1410.37045arXiv1603.01116MaRDI QIDQ3121243

Magnus Aspenberg, Tomas Persson

Publication date: 15 March 2019

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.01116

zbMATH Keywords

large deviationsbounded distortiontopological pressure

Mathematics Subject Classification ID

Dynamical systems involving maps of the interval (37E05) Dimension theory of smooth dynamical systems (37C45)

Related Items

On the intersection of dynamical covering sets with fractals, SHRINKING TARGET PROBLEM FOR RANDOM IFS, The Dolgopyat inequality in bounded variation for non-Markov maps, Shrinking targets and eventually always hitting points for interval maps, Inhomogeneous potentials, Hausdorff dimension and shrinking targets

Cites Work

• Distribution of full cylinders and the Diophantine properties of the orbits in \(\beta\)-expansions
• Typical points and families of expanding interval mappings
• Typical points for one-parameter families of piecewise expanding maps of the interval
• The dynamics of the Hénon map
• Diophantine analysis in beta-dynamical systems and Hausdorff dimensions
• Rational Misiurewicz maps are rare
• On iterations of \(1-\alpha x^2\) on \((-1,1)\)
• Complex dynamics
• Decay of correlations for piecewise expanding maps.
• The ergodic theory of shrinking targets
• The Collet-Eckmann condition for rational functions on the Riemann sphere
• Diophantine approximation of the orbit of 1 in the dynamical system of beta expansions
• Uniform Diophantine approximation related to -ary and -expansions
• A multifractal mass transference principle for Gibbs measures with applications to dynamical Diophantine approximation
• On shrinking targets for piecewise expanding interval maps
• Beta-Expansions with Negative Bases
• Some properties of absolutely continuous invariant measures on an interval
• Some Metric Properties of Piecewise Monotonic Mappings of the Unit Interval
• Local dimension for piecewise monotonic maps on the interval
• Dynamical properties of the negative beta-transformation
• Diophantine approximation by orbits of expanding Markov maps
• A NOTE ON INHOMOGENEOUS DIOPHANTINE APPROXIMATION IN BETA-DYNAMICAL SYSTEM
• Dyadic Diophantine approximation and Katok's horseshoe approximation
• Invariant densities for generalizedβ-maps