EUDML

For continuous maps of an interval into itself we consider cycles (periodic orbits) that are non-reducible in the sense that there is no non-trivial partition into blocks of consecutive points permuted by the map. Among them we identify the miror ones. They are those whose existence does not imply existence of other non-reducible cycles of the same period. Moreover, we find minor patterns of a given period with minimal entropy.

Topological conditional entropy

Michał Misiurewicz — 1976

Studia Mathematica

Absolutely continuous invariant measures for maps with flat tops

Michael Benedicks; Michal Misiurewicz — 1989

Publications Mathématiques de l'IHÉS

Rotation sets and ergodic measures for torus homeomorphisms

Michał Misiurewicz; Krystyna Ziemian — 1991

Fundamenta Mathematicae

Fixed points for positive permutation braids

Michał Misiurewicz; Ana Rodrigues — 2012

Fundamenta Mathematicae

Making use of the Nielsen fixed point theory, we study a conjugacy invariant of braids, which we call the level index function. We present a simple algorithm for computing it for positive permutation cyclic braids.

Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval

Sergiĭ Kolyada; Michał Misiurewicz; L’ubomír Snoha — 1999

Fundamenta Mathematicae

The topological entropy of a nonautonomous dynamical system given by a sequence of compact metric spaces ${(X_{i})}_{i = 1}^{\infty}$ and a sequence of continuous maps ${(f_{i})}_{i = 1}^{\infty}$ , $f_{i} : X_{i} \to X_{i + 1}$ , is defined. If all the spaces are compact real intervals and all the maps are piecewise monotone then, under some additional assumptions, a formula for the entropy of the system is obtained in terms of the number of pieces of monotonicity of $f_{n} ○ . . . ○ f_{2} ○ f_{1}$ . As an application we construct a large class of smooth triangular maps of the square of type $2^{\infty}$ and positive...