The fractal dimension of invariant subsets for piecewise monotonic maps on the interval.
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 iterates are not dense in .
The real 3x+1 problem
The stability of Markov operators on Polish spaces
A sufficient condition for the asymptotic stability of Markov operators acting on measures defined on Polish spaces is presented.
The structure of iteration groups of continuous functions. (Summary).
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 .
Topological conjugacies of piecewise monotone interval maps.
Topological invariance of the Collet–Eckmann property for S-unimodal maps
We prove that if f, g are smooth unimodal maps of the interval with negative Schwarzian derivative, conjugated by a homeomorphism of the interval, and f is Collet-Eckmann, then so is g.
Triangular maps with the chain recurrent points periodic.
Turbulent maps and their ω-limit sets
One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.
Two kinds of chaos and relations between them.
Typical continuous function without cycles is stable
Über die multiplikative Translationsgleichung und idempotente Potenzreihenvektoren.
Une propriété extrémale de la suite de Thue-Morse en rapport avec les cascades de Feigenbaum
Uniqueness of regular similarity functions
Variants of Karamata's Iteration Theorem
Vector-valued fractal interpolation functions and their box dimension.
Wandering Sets for a Class of Borel Isomorphisms of ...0,1).
Weakly almost periodic mappings on one- and two-manifolds