Colloquium: Jan Boronski

Please note: MONDAY ROOM 249

Speaker: Jan Boronski, National Supercomputing Center IT4 Innovations Institute for Research and Applications of Fuzzy Modeling, Ostrava, Czech Republic

Title: More on constructions of R.H. Bing’s pseudo-circle in surface dynamics

Abstract: Motivated by the results in [1], we study circle maps f that give the pseudo-circle as the inverse limit space. We show that any such map exhibits the following properties: (1) there exists an entropy set for f with infinite topological entropy, (2) the rotation set is a nondegenerate interval. This shows that the Anosov-Katok type constructions of the pseudo-circle as a minimal set in volume-preserving smooth dynamical systems, or in complex dynamics, obtained previously by Handel, Herman and Chéritat cannot be modeled on inverse limits. This also relates to a known fact for Hénon-type attractors: R.F. Williams showed that every hyperbolic, one-dimensional, expanding attractor for a discrete dynamical system is topologically conjugate to the induced map on an inverse limit space based on a branched one-manifold, but M. Barge proved that certain dynamical systems with Hénon-type attractors cannot be modeled on inverse limits.

[1] Boronski J.P.; Oprocha P., Rotational chaos and strange attractors on the 2-torus, Mathematische Zeitschrift, (2015) 279:689--702, DOI10.1007/s00209-014-1388-1

Faculty hosts: Krystyna Kuperberg and Michel Smith