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- W3205938392 abstract "The paper is devoted to an investigation of the genus of an orientable closed surface $M^{2}$ which admits $A$-endomorphisms whose nonwandering set contains a one-dimensional strictly invariant contracting repeller $Lambda_{r}$ with a uniquely defined unstable bundle and with an admissible boundary of finite type. First, we prove that, if $M^{2}$ is a torus or a sphere, then $M^{2}$ admits such an endomorphism. We also show that, if $Omega$ is a basic set with a uniquely defined unstable bundle of the endomorphism $fcolon M^{2}to M^{2}$ of a closed orientable surface $M^{2}$ and $f$ is not a diffeomorphism, then $Omega$ cannot be a Cantor type expanding attractor. At last, we prove that, if $fcolon M^{2}to M^{2}$ is an $A$-endomorphism whose nonwandering set consists of a finite number of isolated periodic sink orbits and a one-dimensional strictly invariant contracting repeller of Cantor type $Omega_{r}$ with a uniquely defined unstable bundle and such that the lamination consisting of stable manifolds of $Omega_{r}$ is regular, then $M^{2}$ is a two-dimensional torus $mathbb{T}^{2}$ or a two-dimensional sphere $mathbb{S}^{2}$." @default.
- W3205938392 created "2021-10-25" @default.
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- W3205938392 date "2021-01-01" @default.
- W3205938392 modified "2023-10-17" @default.
- W3205938392 title "Cantor Type Basic Sets of Surface $A$-endomorphisms" @default.
- W3205938392 doi "https://doi.org/10.20537/nd210307" @default.
- W3205938392 hasPublicationYear "2021" @default.
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