L’ubomír Snoha

There are no piecewise linear maps of type 2

The aim of this paper is to show that there are no piecewise linear maps of type 2∞. For this purpose we use the fact that any piecewise monotone map of type 2∞ has an infinite ω-limit set which is a subset of a doubling period solenoid. Then we prove that piecewise linear maps cannot have any doubling period solenoids.

Proper minimal sets on compact connected 2-manifolds are nowhere dense

Let M 2 be a compact connected two-dimensional manifold, with or without boundary, and let f : M 2 ! M 2 be a continuous map. We prove that if M M 2 is a minimal set of the dynamical system (M 2 , f ) then either M = M 2 or M is a nowhere dense subset of M 2 . Moreover, we add a shorter proof of the recent result of Blokh, Oversteegen and Tymchatyn, that in the former case M 2 is a torus or a Klein bottle.

For graph maps, one scrambled pair implies Li-Yorke chaos

For a dynamical system

All maps of type 2^{∞} are boundary maps

(X,f)

Minimal sets of fibre-preserving maps in graph bundles

,

Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval

X

Minimal Spaces with Cyclic Group of Homeomorphisms

being a compact metric space with metric

Spaces of transitive interval maps

d

All solenoids of piecewise smooth maps are period doubling

and

A quantitative approach to transitivity and mixing

f