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.