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Locally connected exceptional minimal sets of surface homeomorphisms

Andrzej Biś, Hiromichi Nakayama, Pawel Walczak (2004)

Annales de l’institut Fourier

We deal with locally connected exceptional minimal sets of surface homeomorphisms. If the surface is different from the torus, such a minimal set is either finite or a finite disjoint union of simple closed curves. On the torus, such a set can admit also a structure similar to that of the Sierpiński curve.

Locally equicontinuous dynamical systems

Eli Glasner, Benjamin Weiss (2000)

Colloquium Mathematicae

A new class of dynamical systems is defined, the class of “locally equicontinuous systems” (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in l ( ) form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems....

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