arXiv subjects

Andres Koropecki

Publications and source records attributed to Andres Koropecki.

20 records · Page 2Linked to original sources

arXiv2009

A mixing-like property and inexistence of invariant foliations for minimal diffeomorphisms of the 2-torus

We consider diffeomorphisms in the $C^\infty$-closure of the conjugancy class of translations of the 2-torus. By a theorem of Fathi and Herman, a generic diffeomorphism in that space is minimal and uniquely ergodic. We define a new mixing-like property, which takes into account the "directions" of mixing, and we prove that generic elements of the space in question satisfy this property. As a consequence, we show that there is a residual set of strictly ergodic diffeomorphisms without invariant foliations of any kind. We also obtain an analytic version of these results.

math.DS↗

arXiv2007

Free curves and periodic points for torus homeomorphisms

We study the relationship between free curves and periodic points for torus homeomorphisms in the homotopy class of the identity. By free curve we mean a homotopically nontrivial simple closed curve that is disjoint from its image. We prove that every rational point in the rotation set is realized by a periodic point provided that there is no free curve and the rotation set has empty interior. This gives a topological version of a theorem of Franks. Using this result, and inspired by a theorem of Guillou, we prove a version of the Poincaré-Birkhoff Theorem for torus homeomorphisms: in the absence of free curves, either there is a fixed point or the rotation set has nonempty interior.

math.DS↗