Tangent Measure Distributions of Hyperbolic Cantor Sets.
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 existence of an a.c.i.p.m. for an expanding map of the interval; the study of a counterexample
The Feigenbaum functional equation and periodic points.
The Feigenbaum functional equation and periodic points. (Short Communication).
The fundamental theorem of dynamical systems
We propose the title of The Fundamental Theorem of Dynamical Systems for a theorem of Charles Conley concerning the decomposition of spaces on which dynamical systems are defined. First, we briefly set the context and state the theorem. After some definitions and preliminary results, based both on Conley's work and modifications to it, we present a sketch of a proof of the result in the setting of the iteration of continuous functions on compact metric spaces. Finally, we claim that this theorem...
The second-order quadratic family.
The structure of Lorenz attractors
The structure of -limit sets for continuous maps of the interval
We prove that every infinite nowhere dense compact subset of the interval is an -limit set of homoclinic type for a continuous function from to .
Topology and dynamics of unstable attractors
This article aims to explore the theory of unstable attractors with topological tools. A short topological analysis of the isolating blocks for unstable attractors with no external explosions leads quickly to sharp results about their shapes and some hints on how Conley's index is related to stability. Then the setting is specialized to the case of flows in ℝⁿ, where unstable attractors are seen to be dynamically complex since they must have external explosions.