Teorie deterministického chaosu a některé její aplikace (1. část)
Teorie deterministického chaosu a některé její aplikace (2. část)
The Art and Science of Symmetric Design
The attractors of the common differential operator are determined by hyperbolic and lacunary functions.
The Bernoulli shift as a basic chaotic dynamical system
We give a brief introduction to the Bernoulli shift map as a basic chaotic dynamical system. We give several examples where the iterates of a~mapping can be understood using the Bernoulli shift. Namely, the iteration of real interval maps and iteration of quadratic functions in the complex plain.
The bitransitive continuous maps of the interval are conjugate to maps extremely chaotic a. e.
The Conley index and countable decompositions of invariant sets
We define a new cohomological index of Conley type associated to any bi-infinite sequence of neighborhoods that satisfies a certain isolation condition. We use this index to study the chaotic dynamics on invariant sets which decompose as countable unions of pairwise disjoint (mod 0) compact pieces.
The coupling of dynamics in couplied map lattices.
The cyclic spectrum of a Boolean flow.
The dimension of the boundary of the Lévy dragon.
The four positive vortices problem : regions of chaotic behavior and the non-integrability
The homeomorphism group of the hairy arc
The size of scrambled sets: n-dimensional case
The structure of Lorenz attractors
The study of the chaotic behavior in retailer's demand model.
Theory of adaptive adjustment.
Thermodynamic formalism, topological pressure, and escape rates for critically non-recurrent conformal dynamics
We show that for critically non-recurrent rational functions all the definitions of topological pressure proposed in [12] coincide for all t ≥ 0. Then we study in detail the Gibbs states corresponding to the potentials -tlog|f'| and their σ-finite invariant versions. In particular we provide a sufficient condition for their finiteness. We determine the escape rates of critically non-recurrent rational functions. In the presence of parabolic points we also establish a polynomial rate of appropriately...
Topological entropy and variation for transitive maps
Topological sequence entropy for maps of the circle
A continuous map of the interval is chaotic iff there is an increasing sequence of nonnegative integers such that the topological sequence entropy of relative to , , is positive ([FS]). On the other hand, for any increasing sequence of nonnegative integers there is a chaotic map of the interval such that ([H]). We prove that the same results hold for maps of the circle. We also prove some preliminary results concerning topological sequence entropy for maps of general compact metric...
Trajectory sensitivity method and master-slave synchronization to estimate parameters of nonlinear systems.