Geodesic
On Two-Dimensional Diffeomorphisms with Homoclinic Orbits to Nonhyperbolic Fixed Points
Russian journal of nonlinear dynamics, Tome 20 (2024) no. 1, pp. 151-165

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We consider two-dimensional diffeomorphisms with homoclinic orbits to nonhyperbolic fixed points. We assume that the point has arbitrary finite order degeneracy and is either of saddle- node or weak saddle type. We consider two cases when the homoclinic orbit is transversal and when a quadratic homoclinic tangency takes place. In the first case we give a complete description of orbits entirely lying in a small neighborhood of the homoclinic orbit. In the second case we study main bifurcations in one-parameter families that split generally the homoclinic tangency but retain the degeneracy type of the fixed point.
Keywords: saddle-node, nonhyperbolic saddle, hyperbolic set, topological Bernoulli scheme
Mots-clés : homoclinic orbit, bifurcation 
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     author = {S. V. Gonchenko and O. V. Gordeeva},
     title = {On {Two-Dimensional} {Diffeomorphisms} with {Homoclinic} {Orbits} to {Nonhyperbolic} {Fixed} {Points}},
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S. V. Gonchenko; O. V. Gordeeva. On Two-Dimensional Diffeomorphisms with Homoclinic Orbits to Nonhyperbolic Fixed Points. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 1, pp. 151-165. http://geodesic.mathdoc.fr/item/ND_2024_20_1_a9/