V. S. Gonchenko

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|Bifurcations of periodic orbits are studied for two-dimensional diieomorphisms close to a diieomorphism with the quadratic homoclinic tangency to a saddle xed point whose Jacobian is equal to one. Problems of the coexistence of periodic orbits of various types of stability are considered. INTRODUCTION It is well known that homoclinic bifurcations of(More)
We study two-parameter bifurcation diagrams of the generalized Hénon map (GHM), that is known to describe dynamics of iterated maps near homoclinic and heteroclinic tangencies. We prove the nondegeneracy of codim 2 bifurcations of fixed points of GHM analytically and compute its various global and local bifurcation curves numerically. Special attention is(More)
We study bifurcations of xed points of rst return maps in two-parameter families of three-dimensional diieomorphisms close to a diieomorphism with a codimension two homoclinic tangency. We suppose that the initial dif-feomorphism has a saddle xed point O with multipliers 1 ; 2 ; such that 0 < j 2 j < j 1 j < 1 < jj and j 1 2 j < 1; the invariant manifolds W(More)
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