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

Roots of continuous piecewise monotone maps of an interval.

Blokh, A.; Coven, E.; Misiurewicz, Michał; Nitecki, Zbigniew — 1991

Acta Mathematica Universitatis Comenianae. New Series

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...

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Irrational life.

Absolutely continuous measures for certain maps of an interval

Structure of mappings of an interval with zero entropy

A Short Proof of the Variational Principle for a $ℤ_{+}^{N}$ Action on a Compact Space

Persistent rotation intervals for old maps

Jumps of entropy in one dimension

Embedding inverse limits interval maps as attractors

Minor cycles for interval maps

Topological conditional entropy

Roots of continuous piecewise monotone maps of an interval.

Absolutely continuous invariant measures for maps with flat tops

Rotation sets and ergodic measures for torus homeomorphisms

Fixed points for positive permutation braids

Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval