Open AccessCombinatorial invariant of Morse-Smale diffeomorphisms on surfaces with orientable heteroclinic
Author(s) -
Морозов Андрей Игоревич,
Починка Ольга Витальевна
Publication year - 2020
Publication title -
žurnal srednevolžskogo matematičeskogo obŝestva
Language(s) - English
Resource type - Journals
eISSN - 2587-7496
pISSN - 2079-6900
DOI - 10.15507/2079-6900.22.202001.71-80
Subject(s) - diffeomorphism , invariant (physics) , surface (topology) , morse code , graph , mathematics , heteroclinic cycle , combinatorics , orientation (vector space) , class (philosophy) , pure mathematics , computer science , geometry , physics , artificial intelligence , bifurcation , homoclinic orbit , telecommunications , nonlinear system , quantum mechanics , mathematical physics
In this paper we consider class of orientation-preserving Morse-Smale diffeomorphisms f, given on orientable surface M2. In their articles A.A.~Bezdenezhnich and V. Z. Grines has shown, that such diffeomorfisms contain finite number of heteroclinic orbits. Moreover, the problem of classification for such diffeomorphisms is reduced to the problem of distinguishing orientable graphs with substitutions describing the geometry of heteroclinic intersections. Howewer, these graphs generally do not allow polynomial distinguishing algorithms. In this paper, we propose a new approach to the classification of such cascades. To this end, each considered diffeomorphism f is associated with a graph whose embeddablility in the ambient surface makes it possible to construct an effective algoritm for distinguishing such graphs.