ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

A Method for Investigation of a Neighborhood of a Nontransverse Homoclinic Point of a Two-dimensional Diffeomorphism


S. B. Tikhomirov

Russia, 195251, Saint-Petersburg, Bibliotechnaya pl., 2,
St. Petersburg State University,
Faculty of Mathematics and Mecanics


A nontransverse homoclinic points of a hyperbolic saddle fixed point of a two-dimensional diffeomorphism is considered. It is assumed that the saddle value is less than 1. A new proof of the existence of a countable set of periodic points in a small neighborhood is presented. For the case of quadratic tangency, hyperbolicity of the obtained periodic points is proved and the existence of a transverse heteroclinic structure is established.

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