Page 1 Next

Displaying 1 – 20 of 59

Showing per page

A Proof of Simultaneous Linearization with a Polylog Estimate

Tomoki Kawahira (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

We give an alternative proof of simultaneous linearization recently shown by T. Ueda, which connects the Schröder equation and the Abel equation analytically. In fact, we generalize Ueda's original result so that we may apply it to the parabolic fixed points with multiple petals. As an application, we show a continuity result on linearizing coordinates in complex dynamics.

Accessibility of typical points for invariant measures of positive Lyapunov exponents for iterations of holomorphic maps

Feliks Przytycki (1994)

Fundamenta Mathematicae

We prove that if A is the basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, if A is completely invariant (i.e. f - 1 ( A ) = A ), and if μ is an arbitrary f-invariant measure with positive Lyapunov exponents on ∂A, then μ-almost every point q ∈ ∂A is accessible along a curve from A. In fact, we prove the accessibility of every “good” q, i.e. one for which “small neigh bourhoods arrive at large scale” under iteration of f. This generalizes the...

Branched coverings and cubic Newton maps

Lei Tan (1997)

Fundamenta Mathematicae

We construct branched coverings such as matings and captures to describe the dynamics of every critically finite cubic Newton map. This gives a combinatorial model of the set of cubic Newton maps as the gluing of a subset of cubic polynomials with a part of the filled Julia set of a specific polynomial (Figure 1).

Compacts connexes invariants par une application univalente

Emmanuel Risler (1999)

Fundamenta Mathematicae

Let K be a compact connected subset of cc, not reduced to a point, and F a univalent map in a neighborhood of K such that F(K) = K. This work presents a study and a classification of the dynamics of F in a neighborhood of K. When ℂ K has one or two connected components, it is proved that there is a natural rotation number associated with the dynamics. If this rotation number is irrational, the situation is close to that of “degenerate Siegel disks” or “degenerate Herman rings” studied by R. Pérez-Marco...

Complex one-frequency cocycles

Artur Avila, Svetlana Jitomirskaya, Christian Sadel (2014)

Journal of the European Mathematical Society

We show that on a dense open set of analytic one-frequency complex valued cocycles in arbitrary dimension Oseledets filtration is either dominated or trivial. The underlying mechanism is different from that of the Bochi-Viana Theorem for continuous cocycles, which links non-domination with discontinuity of the Lyapunov exponent. Indeed, in our setting the Lyapunov exponents are shown to depend continuously on the cocycle, even if the initial irrational frequency is allowed to vary. On the other...

Control a state-dependent dynamic graph to a pre-specified structure

Fei Chen, Zengqiang Chen, Zhongxin Liu, Zhuzhi Yuan (2009)


Recent years have witnessed an increasing interest in coordinated control of distributed dynamic systems. In order to steer a distributed dynamic system to a desired state, it often becomes necessary to have a prior control over the graph which represents the coupling among interacting agents. In this paper, a simple but compelling model of distributed dynamical systems operating over a dynamic graph is considered. The structure of the graph is assumed to be relied on the underling system's states....

Density of periodic sources in the boundary of a basin of attraction for iteration of holomorphic maps: geometric coding trees technique

Feliks Przytycki, Anna Zdunik (1994)

Fundamenta Mathematicae

We prove that if A is a basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, then the periodic points in the boundary of A are dense in this boundary. To prove this in the non-simply connected or parabolic situations we prove a more abstract, geometric coding trees version.

Distributional chaos of time-varying discrete dynamical systems

Lidong Wang, Yingnan Li, Yuelin Gao, Heng Liu (2013)

Annales Polonici Mathematici

This paper is concerned with distributional chaos of time-varying discrete systems in metric spaces. Some basic concepts are introduced for general time-varying systems, including sequentially distributive chaos, weak mixing, and mixing. We give an example of sequentially distributive chaos of finite-dimensional linear time-varying dynamical systems, which is not distributively chaotic of type i (DCi for short, i = 1, 2). We also prove that two uniformly topological equiconjugate time-varying systems...

Dynamical behavior of two permutable entire functions

Kin-Keung Poon, Chung-Chun Yang (1998)

Annales Polonici Mathematici

We show that two permutable transcendental entire functions may have different dynamical properties, which is very different from the rational functions case.

Dynamical properties of some classes of entire functions

A. Eremenko, M. Yu Lyubich (1992)

Annales de l'institut Fourier

The paper is concerned with the dynamics of an entire transcendental function whose inverse has only finitely many singularities. It is rpoven that there are no escaping orbits on the Fatou set. Under some extra assumptions the set of escaping orbits has zero Lebesgue measure. If a function depends analytically on parameters then a periodic point as a function of parameters has only algebraic singularities. This yields the Structural Stability Theorem.

Currently displaying 1 – 20 of 59

Page 1 Next