Pesin’s dimension for Poincaré recurrences
- 1 March 1997
- journal article
- research article
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 7 (1) , 12-20
- https://doi.org/10.1063/1.166237
Abstract
A new characteristic of Poincare recurrences is introduced. It describes an average return time in the framework of a general construction for dimension-like characteristics. Some examples are considered including rotations on the circle and the Denjoy example. (C) 1997 American Institute of Physics.Keywords
This publication has 7 references indexed in Scilit:
- Self-similarity, renormalization, and phase space nonuniformity of Hamiltonian chaotic dynamicsChaos: An Interdisciplinary Journal of Nonlinear Science, 1997
- Connection between recurrence-time statistics and anomalous transportPhysical Review Letters, 1991
- Dimension type characteristics for invariant sets of dynamical systemsRussian Mathematical Surveys, 1988
- Global Universality at the Onset of Chaos: Results of a Forced Rayleigh-Bénard ExperimentPhysical Review Letters, 1985
- The infinite number of generalized dimensions of fractals and strange attractorsPhysica D: Nonlinear Phenomena, 1983
- Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximationTheory of Computing Systems, 1967
- ber die simultanen diophantischen ApproximationenMathematische Zeitschrift, 1931