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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2021 Volume 212, Number 5, Pages 102–132 (Mi sm9372)

This article is cited in 2 papers

On $DA$-endomorphisms of the two-dimensional torus

V. Z. Grines, E. V. Zhuzhoma, E. D. Kurenkov

National Research University Higher School of Economics, Nizhnii Novgorod, Russia

Abstract: It is proved that in each homotopy class of continuous mappings of the two-dimensional torus to itself that induce a hyperbolic action on the fundamental group, as long as it is free of expanding mappings, there exists an $A$-endomorphism $f$ whose nonwandering set consists of an attracting hyperbolic sink and a nontrivial one-dimensional collapsing repeller, which is a one-dimensional orientable lamination, locally homeomorphic to the direct product of a Cantor set and a line segment. Moreover, the unstable $Df$-invariant subbundle of the tangent space to the repeller has the property of uniqueness.
Bibliography: 23 titles.

Keywords: $A$-endomorphism, repeller, wandering set.

UDC: 517.938

MSC: 37C70, 37D20

Received: 21.01.2020 and 07.07.2020

DOI: 10.4213/sm9372


 English version:
Sbornik: Mathematics, 2021, 212:5, 698–725

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© Steklov Math. Inst. of RAS, 2024