Teorie deterministického chaosu a některé její aplikace (1. část)
Teorie deterministického chaosu a některé její aplikace (2. část)
Teorie dynamických systémů
The -complex Bruno function and the Yoccoz function: a numerical study of the Marmi-Moussa-Yoccoz conjecture.
The Abramov-Rokhlin Entropy Addition Formula for Amenable Group Actions.
The asymptotics of the Perron-Frobenius operator of a class of interval maps preserving infinite measures
We determine the asymptotic behaviour of the iterates of the Perron-Frobenius operator for specific interval maps with an indifferent fixed point which gives rise to an infinite invariant measure.
The Billiard in a Regular Polygon.
The bitransitive continuous maps of the interval are conjugate to maps extremely chaotic a. e.
The branch locus for one-dimensional Pisot tiling spaces
If φ is a Pisot substitution of degree d, then the inflation and substitution homeomorphism Φ on the tiling space factors via geometric realization onto a d-dimensional solenoid. Under this realization, the collection of Φ-periodic asymptotic tilings corresponds to a finite set that projects onto the branch locus in a d-torus. We prove that if two such tiling spaces are homeomorphic, then the resulting branch loci are the same up to the action of certain affine maps on the torus.
The centralizer of Morse shifts
The centralizer of Morse shifts induced by arbitrary blocks
The classification of tiling space flows.
The coexistence problem" for conservative dynamical systems: a review
The cohomological equation for area-preserving flows on compact surfaces.
The Convergence of Zeta Functions for Certain Geodesic Flow Depends on Their Pressure.
The Dynamical Complexity of Orientation Reversing Homeomorphisms of Surfaces.
The dynamics of piecewise monotonic maps under small perturbations
The entropy function on an algebraic structure with infinite partition and -preserving transformation generators.
The entropy of algebraic actions of countable torsion-free abelian groups
This paper is concerned with the entropy of an action of a countable torsion-free abelian group G by continuous automorphisms of a compact abelian group X. A formula is obtained that expresses the entropy in terms of the Mahler measure of a greatest common divisor, complementing earlier work by Einsiedler, Lind, Schmidt and Ward. This leads to a uniform method for calculating entropy whenever G is free. In cases where these methods do not apply, a possible entropy formula is conjectured. The entropy...
The existence of an a.c.i.p.m. for an expanding map of the interval; the study of a counterexample