Seminar za dinamičke sustave

lokacija: 
PMF Matematički odsjek (virtualno)
vrijeme: 
16.02.2021 - 16:15 - 18:00
On Tuesday, 16/02/2021, at 16.15,

Jan P. Boroński, AGH University of Science and Technology, Kraków, will give a talk in Dynamical Systems Seminar in Zagreb under the title:

 

Crovisier-Pujals-like 1-dimensional models for Lozi maps within the Misiurewicz parameter set

Abstract: In my talk I shall discuss my recent work with S. Stimac on parametric families of dissipative homeomorphisms on surfaces [5]. Our starting point was recent novel approach by Crovisier and Pujals [1], in which they introduced the notion of Strongly Dissipative Diffeomorphisms (see also [2]). These maps are shown in [1] to be very close in a certain sense to 1-dimensional maps. In particular, Crovisier and Pujals showed that for any of them there exists a reduction to a 1-dimensional model, that consists of a metric tree and continuous map that is semi-conjugate to the original diffeomorphism. They also showed that the class of strongly dissipative diffeomorphisms contains maps in the Hénon family, for an open set of parameters. We construct a Crovisier-Pujals-like 1-dimensional model for the Lozi family of maps [3], within the Misiurewicz parameter set [4]. This model conjugates each Lozi map in the studied parameter set to the natural extension of a continuous map on a metric tree with a dense set of branching points. Some aspect of our study apply also to certain elements of the Crovisier-Pujals open set within Henon family.

References:
[1] S. Crovisier, E. Pujals, Strongly dissipative surface diffeomorphisms, Commentarii Mathematici Helvetici 93 (2018), 377–400.
[2] S. Crovisier, E. Pujals, C, Tresser, Mild dissipative diffeomorphisms of the disk with zero entropy, arXiv 2020.
[3] R. Lozi, Un attracteur etrange(?) du type attracteur de H ́enon, J. Physique (Paris) 39 (Coll. C5) (1978), 9–10.
[4] M. Misiurewicz, Strange attractor for the Lozi mappings, Ann. New York Acad. Sci. 357 (1980), 348–358.

[5] Topological and Smooth Dynamics on Surfaces, Mathematisches Forschungsinstitut Oberwolfach Report No. 27/2020, DOI: 10.4171/OWR/2020/27

 

The talk will be held via Zoom platform:

 
Topic: Seminar DYNSYS
 
Meeting ID: 881 5457 8830

Everybody is invited.

 

Maja Resman

 

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