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Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua

100%

Kwapisz J.

Fundamenta Mathematicae

2001

tom 168

nr 3

251-278

We describe the homotopy classes of self-homeomorphisms of solenoids and Knaster continua. In particular, we demonstrate that homeomorphisms within one homotopy class have the same (explicitly given) topological entropy and that they are actually semi-conjugate to an algebraic homeomorphism in the case when the entropy is positive.

Topological friction in aperiodic minimal $ℝ^m$-actions

100%

Kwapisz J.

Fundamenta Mathematicae

2010

tom 207

nr 2

175-178

For a continuous map f preserving orbits of an aperiodic $ℝ^m$-action on a compact space, its displacement function assigns to x the "time" $t ∈ ℝ^m$ it takes to move x to f(x). We show that this function is continuous if the action is minimal. In particular, f is homotopic to the identity along the orbits of the action.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Kwapisz J.

1 2010

1 2001

Wyniki wyszukiwania

Homotopy and dynamics for homeomorphisms of solenoids and Knaster continua

Topological friction in aperiodic minimal $ℝ^m$-actions