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DynamIC Seminars
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Andrey Morozov (HSE Nizhny Novgorod)
Realization of homeomorphisms of surfaces of algebraically finite order by Morse-Smale diffeomorphisms with orientable heteroclinic intersection
Abstract:
According to Thurston's classification, the set of homotopy classes of homeomorphisms defined on closed orientable surfaces of negative curvature is split into four disjoint subsets. A homotopy class from each subset is characterized by the existence in it of a homeomorphism called the Thurston canonical form and which is exactly one of the following types, respectively: a periodic homeomorphism, reducible nonperiodic homeomorphism of algebraically finite order, a reducible homeomorphism that is not a algebraically finite order homeomorphism, a pseudo-anosov homeomorphism. Thurston's canonical forms are not structurally stable diffeomorphisms. Therefore, the problem naturally arises of constructing the simplest (in a certain sense) structurally stable diffeomorphisms in each homotopy class. In each homotopy class from the first subset A.N. Bezdezhnykh and V.Z. Grines constructed a gradient-like diffeomorphism. R.V. Plykin and A. Yu. Zhirov announced a method for constructing a structurally stable diffeomorphism in each homotopy class from the fourth subset. The non-wandering set of this diffeomorphism consists of a finite number of source orbits and a single one-dimensional attractor. In this paper, we describe the construction of a structurally stable diffeomorphism in each homotopy class from the second subset. The constructed representative is a Morse-Smale diffeomorphism with an orientable heteroclinic intersection.
Tuesday, 30 November 2021
13:00
Online
Isaia Nisoli (Universidade Federal de Rio de Janeiro)
TBA
Abstract:
TBA
Tuesday, 7 December 2021
13:00
Online
Emilio Corso (ETH Zurich)
TBA
Abstract:
TBA
Tuesday, 14 December 2021
13:00
Online
DynamIC Workshops and Mini-Courses
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Date
Venue
Online Workshop on Critical Transitions in Complex Systems
Wednesday, 29 July 2020 – Friday, 31 July 2020
online
Workshop on Critical Transitions in Complex Systems
Monday, 25 March 2019 – Friday, 29 March 2019
Imperial College London
Workshop on Random Dynamical Systems
Wednesday, 20 March 2019 – Friday, 22 March 2019
Imperial College London
Symposium on Machine Learning and Dynamical Systems
Monday, 11 February 2019 – Wednesday, 13 February 2019
Imperial College London
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