Gonchenko, S. V.; Shil’nikov, L. P. On geometrical properties of two-dimensional diffeomorphisms with homoclinic tangencies. (English) Zbl 0885.58062 Int. J. Bifurcation Chaos Appl. Sci. Eng. 5, No. 3, 819-829 (1995). Summary: Two-dimensional diffeomorphisms with a quadratic tangency of invariant manifolds of a saddle fixed point are considered in the cases where the saddle value \(\sigma\) is either less than 1 or equal to it. A description of the structure of hyperbolic subsets is given. In the case \(\sigma=1\), it is shown that almost all such diffeomorphisms admit the complete description in distinction with the case \(\sigma<1\). Cited in 8 Documents MSC: 37D99 Dynamical systems with hyperbolic behavior 37G99 Local and nonlocal bifurcation theory for dynamical systems 37C75 Stability theory for smooth dynamical systems Keywords:two-dimensional diffeomorphisms; homoclinic tangencies × Cite Format Result Cite Review PDF Full Text: DOI