Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки

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Title of Article

ON BIFURCATIONS OF TWO-DIMENSIONAL DIFFEOMORPHISMS WITH A HOMOCLINIC TANGENCY TO A SADDLE-NODE FIXED POINT

Issue
Date

Article type	scientific article	UDC	517.917
Pages	198-209	Keywords

Authors

R“RѕRЅS‡RµRЅRєRѕ RЎ.R’.RќReR¶RµRіRѕSЂRѕRґSЃRєReR№ RіRѕSЃSѓRЅReRІRµSЂSЃReS‚RµS‚ ReRј. Rќ.R?. R›RѕR±R°S‡RµRІSЃRєRѕRіRѕ
R“RѕSЂRґRµRµRІR° Rћ.R’.RќReR¶RµRіRѕSЂRѕRґSЃRєReR№ RіRѕSЃSѓRЅReRІRµSЂSЃReS‚RµS‚ ReRј. Rќ.R?. R›RѕR±R°S‡RµRІSЃRєRѕRіRѕ
R›SѓRєSЊSЏRЅRѕRІ R’.R?.RќReR¶RµRіRѕSЂRѕRґSЃRєReR№ RіRѕSЃSѓRЅReRІRµSЂSЃReS‚RµS‚ ReRј. Rќ.R?. R›RѕR±R°S‡RµRІSЃRєRѕRіRѕ
RћRІSЃSЏRЅRЅReRєRѕRІ R?.R?.RќReR¶RµRіRѕSЂRѕRґSЃRєReR№ RіRѕSЃSѓRЅReRІRµSЂSЃReS‚RµS‚ ReRј. Rќ.R?. R›RѕR±R°S‡RµRІSЃRєRѕRіRѕ

Abstract

We study main bifurcations of two-dimensional diffeomorphisms having a quadratic homoclinic tangency to a saddle-node fixed point. The bifurcation diagram for single-round periodic orbits from a small fixed neighborhood of the homoclinic orbit is constructed in the parameter plane. We discuss the relation between the results obtained and the well-known codimension-one bifurcations for the cases of a saddle fixed point with a quadratic homoclinic tangency and a saddle-node fixed point with a transverse homoclinic orbit.

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