Marina Barinova
Publications:
Barinova M. K., Gogulina E. Y., Pochinka O. V.
Omegaclassification of Surface Diffeomorphisms Realizing Smale Diagrams
2021, Vol. 17, no. 3, pp. 321334
Abstract
The present paper gives a partial answer to Smale's question
which diagrams can correspond to $(A,B)$diffeomorphisms.
Model diffeomorphisms of the twodimensional torus derived
by ``Smale surgery'' are considered, and necessary and
sufficient conditions for their topological conjugacy are
found. Also, a class $G$ of $(A,B)$diffeomorphisms on surfaces which are the connected
sum of the model diffeomorphisms is introduced. Diffeomorphisms of the class $G$ realize any connected Hasse
diagrams (abstract Smale graph). Examples of diffeomorphisms from $G$ with isomorphic labeled Smale diagrams which are not ambiently $\Omega$conjugated are constructed. Moreover, a subset $G_{*}^{} \subset G$ of diffeomorphisms for which the isomorphism class of labeled Smale diagrams is a complete invariant of the ambient $\Omega$conjugacy is singled out.
