Discrete Dynamical Systems

this session is held at Faculty of Civil Engineering, room B 365 Thákurova 7

Friday January 22

9:00 - 9:40
Lluis Alseda i Soler (Universitat Autònoma de Barcelona)
A strongly F-invariant pinched core strip that does not contain any arc of curve

In [1] the authors define the concept of pinched core strip. So far it has not been given an example of such an object that is strongly invariant under a quasi-periodic triangular function and it is not a curve. In this talk we will describe how to construct such an example.

[1] R. Fabbri, T. Jäger, R. Johnson and G. Keller, A Sharkovskii-type theorem for minimally forced interval maps, Topological Methods in Nonlinear Analysis, Journal of the Juliusz Shauder Center, 2005(26), 163-188.

9:45 - 10:25
Jaroslav Smítal (Silesian University, Opava)
Distributional chaos - recent results and problems

10:30 - 11:10
Francesc Mañosas (Universitat Autònoma de Barcelona)
Global linearization of periodic recurrences

We deal with m-periodic, n-th order difference equations and study whether they can be globally linearized. We give an affirmative answer when m = n+1 and for most of the known examples appearing in the literature. Our main tool is a refinement of the Montgomery-Bochner Theorem. We also prove some nice features of the (n + 3)-periodic Coxeter difference equations.

11:15 - 11:55
Peter Maličký (Matej Bel University, Banská Bystrica)
The Lotka-Volterra map and some problems of the number theory.

The Lotka-Volterra map is a transformation of the triangle with vertices (0,0),(4,0) and (4,0) given by formula F(x,y)=(x(4-x-y),xy). We show that properties of interior periodic orbits are closely related to some problems of the number theory. Some of these problems are open.

14:15 - 14:55
Anna Cima Mollet (Universitat Autònoma de Barcelona)
Global dynamics of discrete systems through Lie Symmetries

We use the existence of Lie Symmetries to study the discrete dynamics of some rational maps in Rn.

15:00 - 15:40
Michal Kupsa (Academy of Sciences, Prague)
Exponential return times and mixing processes

15:45 - 16:25
Lubomíra Balková (Czech Technical University, Prague)
Generalization of Sturmian Words

Sturmian words are aperiodic words with the lowest possible complexity. No wonder they belong to the most studied infinite words and many equivalent definitions of Sturmian words havee been found out. In our contribution, we will consider the generalizations of their combinatorial definitions and properties to multiliteral alphabets. We will in particular explain the relations between such properties and we will mention interesting open questions. This is a joint work with Štěpán Starosta.

16:30 - 17:10
Matúš Dirbák (Matej Bel University, Banská Bystrica)
Extensions without increasing the entropy as a tool for entropy bounds problem

We show how extensions without increasing the entropy can be used to determine the infimum of topological entropies of all maps with a given property on a given space and present known as well as new results in this direction.

Monday January 25

9:00 - 9:40
Petr Kůrka (Academy of Sciences, Prague)
Moebius number systems

9:45 - 10:25
Xavier Jarque (Universitat Rovira i Virgili, Tarragona)
About the connectivity of the escaping set for entire transcendental maps

Since Eremenko's conjecture (all connected components of the escaping set for transcendental entire maps are unbounded) the study of the connectivity (or not) of the escaping set has been studied in different frameworks. Recently two main results has been proved: On one hand it has been found an example showing that the conjecture is not true even for entire maps in class B for which wall singular values are contained in a compact set (L. Rempe et al). On the other under certain hypotheses (precisely strongly subhyperbolicity) it has been shown that the escaping set is disconnected (H. Mihaljevic-Brandt). We finally discuss recent work about the connectivity of the escaping set for the complex exponential family.

10:30 - 11:10
Armengol Gasull (Universitat Autònoma de Barcelona)
On two and three periodic Lyness difference equations

We describe the sequences xn given by the non-autonomous second order Lyness difference equations xn+2=(an+xn+1)/xn, where an is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x1,x2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations.

11:15 - 11:55
Jozef Bobok (Czech Technical University, Prague)
On nowhere differentiable measure preserving maps

We present several known results on nowhere differentiable measure preserving interval maps and discuss their properties with respect to the topological entropy. Some open problems will also be stated.