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

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

Sbornik. Mathematics, Tome 212 (2021) no. 5, pp. 698-725

Résumé

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.

Détail

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

Bibliographie

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