Abstract:
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.
This work was carried out within the framework of the grant 19-11-00280 of the RSciF. The results from
Section 4 (the proof of Theorem 2) were supported by the grant FSWR-2020-0036 of the Ministry of
Science and Higher Education of the Russian Federation. S. Gonchenko is also supported by the Basic
Research Program at HSE University.
Citation:
S. V. Gonchenko, O. V. Gordeeva, “On Two-Dimensional Diffeomorphisms with Homoclinic Orbits to Nonhyperbolic Fixed Points”, Rus. J. Nonlin. Dyn., 20:1 (2024), 151–165
\Bibitem{GonGor24}
\by S. V. Gonchenko, O. V. Gordeeva
\paper On Two-Dimensional Diffeomorphisms with Homoclinic Orbits to Nonhyperbolic Fixed Points
\jour Rus. J. Nonlin. Dyn.
\yr 2024
\vol 20
\issue 1
\pages 151--165
\mathnet{http://mi.mathnet.ru/nd886}
\crossref{https://doi.org/10.20537/nd231204}
Citation in format AMSBIB
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