English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

It is well-known that there is a close relationship between the dynamics ofdiffeomorphisms satisfying the axiom $A$ and the topology of the ambientmanifold. In the given article, this statement is considered for the class$\mathbb G(M^2)$ of $A$-diffeomorphisms of closed orientable surfaces such thattheir non-wandering set consists of $k_f\geq 2$ connected components ofone-dimensional basic sets (attractors and repellers). We prove that theambient surface of every diffeomorphism $f\in \mathbb G(M^2)$ is homeomorphicto the connected sum of $k_f$ closed orientable surfaces and $l_f$two-dimensional tori such that the genus of each surface is determined by thedynamical properties of appropriating connected component of a basic set and$l_f$ is determined by the number and position of bunches, belonging to allconnected components of basic sets. We also prove that every diffeomorphismfrom the class $\mathbb G(M^2)$ is $\Omega$-stable but is not structurallystable.

On decomposition of ambient surfaces admitting A-diffeomorphisms with nontrivial attractors and repellers