Attractors of homeomorphism groups on manifolds with boundary
https://doi.org/10.26907/2949-3919.2025.3.43-57
Abstract
Let G be the group of homeomorphisms of an n-dimensional topological manifold M with a nonempty boundary ∂M. The aim of this work is to study the effect of the nonempty boundary of the manifold M on the structure of global attractors of the homeomorphism group G. Our main result is the proof that any global attractor A of the homeomorphism group G on a manifold M with a nonempty boundary ∂M either belongs to the boundary and it can be either a proper subset of the boundary or coincide with the boundary, or it is equal to the union of the boundary with the global attractor of the group induced on the interior of the manifold M. It is shown that, generally speaking, non-global attractors do not possess this property. Various examples are constructed, including an example with two different global attractors.
Supporting agencies: This work is an output of a research project implemented as part of the Basic Research Program at the National Research University Higher School of Economics (HSE University).
About the Authors
R. A. Dedaev
HSE University
Russian Federation
Russian Federation
Roman Aleksandrovich Dedaev
25/12 Bolshaya Pecherskaya str., Nizhny Novgorod 603155
N. I. Zhukova
HSE University
Russian Federation
Russian Federation
Nina Ivanovna Zhukova
25/12 Bolshaya Pecherskaya str., Nizhny Novgorod 603155
R. R. Imaev
HSE University
Russian Federation
Russian Federation
Roman Ruslanovich Imaev
25/12 Bolshaya Pecherskaya str., Nizhny Novgorod 603155
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Review
For citations:
Dedaev R.A., Zhukova N.I., Imaev R.R. Attractors of homeomorphism groups on manifolds with boundary. Mathematics and Theoretical Computer Science. 2025;3(3):43-57. (In Russ.) https://doi.org/10.26907/2949-3919.2025.3.43-57
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