Geodesic
Stable periodic points for smooth diffeomorphisms of multidimensional space
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 27-35

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We regard $C^r$-smooth ($r\geqslant1$) self-diffeomorphism of multidimensional space with a hyperbolic fixed point and non-transversal homoclinic point. In the works by Sh. Newhouse, L. P. Shil'nikov, B. F. Ivanov and other authors it is shown that under certain condition on the type of contact of stable and unstable manifolds, the neighborhoods of the homoclinic point may contain a countable set of stable periodic points, but at least one of their characterictic exponents tends to zero with the increase of a period. The goal of this work is to prove that under certain conditions imposed on the character of tangency between the stable and unstable manifolds, the neighborhood of the homoclinic point may contain an infinite set of stable periodic points whose characteristic exponents are negative and bounded away from zero.
Keywords: diffeomorphism of multidimentional space, homoclinic points, stable periodic points. 
@article{VUU_2013_4_a3,
     author = {E. V. Vasil'eva},
     title = {Stable periodic points for smooth diffeomorphisms of multidimensional space},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {27--35},
     publisher = {mathdoc},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2013_4_a3/}
}
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E. V. Vasil'eva. Stable periodic points for smooth diffeomorphisms of multidimensional space. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2013), pp. 27-35. http://geodesic.mathdoc.fr/item/VUU_2013_4_a3/