Parametric families of attractors and inverse limits

Abstract: In my talk I shall discuss some of my recent work on parametric families of maps and their strange attractors on surfaces, which employed inverse limit approach. They were focusing on computing accessible rotation numbers (e.g. for reduced Arnold Standard Family [1]), and building 1-dimensional models that are reductions of 2-dimensional dynamics in the presence of strong (mild) dissipation [2]. The latter was inspired by recent results of Crovisier and Pujals [3] (see also [4]).

References [1] Boroński, J. P.; Činč, J.; Liu, X-C "Prime ends dynamics in parametrised families of rotational attractors". J. Lond. Math. Soc. (2) 102 (2020), no. 2, 557–579. [2] Topological and Smooth Dynamics on Surfaces, Mathematisches Forschungsinstitut Oberwolfach Report No. 27/2020, DOI: 10.4171/OWR/2020/27 [3] S. Crovisier, E. Pujals, "Strongly dissipative surface diffeomorphisms", Commentarii Mathematici Helvetici 93 (2018), 377–400. [4] S. Crovisier, E. Pujals, C, Tresser, "Mild dissipative diffeomorphisms of the disk with zero entropy", arXiv 2020.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University