Geodesic
Necessary and sufficient conditions for the topological conjugacy of surface diffeomorphisms with a~finite number of orbits of heteroclinic tangency
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 198-219

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We consider diffeomorphisms of orientable surfaces with the nonwandering set consisting of a finite number of hyperbolic fixed points and the wandering set containing a finite number of heteroclinic orbits of transversal and nontransversal intersection. We distinguish a meaningful class of diffeomorphisms and present a complete topological invariant for this class. The invariant is a scheme consisting of a set of numerical parameters and a set of geometric objects. 
@article{TM_2010_270_a14,
     author = {T. M. Mitryakova and O. V. Pochinka},
     title = {Necessary and sufficient conditions for the topological conjugacy of surface diffeomorphisms with a~finite number of orbits of heteroclinic tangency},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {198--219},
     publisher = {mathdoc},
     volume = {270},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_270_a14/}
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T. M. Mitryakova; O. V. Pochinka. Necessary and sufficient conditions for the topological conjugacy of surface diffeomorphisms with a~finite number of orbits of heteroclinic tangency. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 198-219. http://geodesic.mathdoc.fr/item/TM_2010_270_a14/