Transversal Homoclinic Orbits near Elliptic Fixed Points of Area-preserving Diffeomorphisms of the Plane
作者： Chr. Genecand
DOI: 10.1007/978-3-642-61232-9_1
关键词:
摘要: Extending a result due to E. Zehnder [27], we prove that generically, an area-preserving analytic diffeomorphism of the plane has transversal homoclinic orbits and nondegenerate Mather sets in every neighborhood stable elliptic fixed point. “Generically” refers topology defined by means Taylor coefficients mapping at point whose order is higher than prescribed arbitrary integer, all lower being held fixed. The proof makes use Aubry-Mather theory for monotone twist mappings.
springer.com
sci-hub.se 参考文章(29)
H. W. Broer, F. Takens, Formally Symmetric Normal Forms and Genericity Dynamics Reported. ,vol. 2, pp. 39- 59 ,(1989) , 10.1007/978-3-322-96657-5_2
J. Moser, Proof of a generalized from of a fixed point theorem due to G. D. Birkhoff Lecture Notes in Mathematics. pp. 464- 494 ,(1977) , 10.1007/BFB0085372
V. Bangert, Mather Sets for Twist Maps and Geodesics on Tori Dynamics Reported. pp. 1- 56 ,(1988) , 10.1007/978-3-322-96656-8_1
Carl-Ludwig Siegel, Jürgen K. Moser, C. I. Kalme, Lectures on Celestial Mechanics ,(1971)
Jerrold Marsden, Philip Holmes, Jürgen Scheurle, Exponentially small splittings of separatrices with applications to KAM theory and degenerate bifurcations American Mathematical Society. ,(1988)
S. Aubry, P.Y. Le Daeron, The discrete Frenkel-Kontorova model and its extensions Physica D: Nonlinear Phenomena. ,vol. 8, pp. 381- 422 ,(1983) , 10.1016/0167-2789(83)90233-6
Helmut R�ssmann, Über die Existenz einer Normalform inhaltstreuer elliptischer Transformationen Mathematische Annalen. ,vol. 137, pp. 64- 77 ,(1959) , 10.1007/BF01343073
Serge Aubry, The twist map, the extended Frenkel-Kontorova model and the devil's staircase Physica D: Nonlinear Phenomena. ,vol. 7, pp. 240- 258 ,(1983) , 10.1016/0167-2789(83)90129-X
John N. Mather, Existence of quasi-periodic orbits for twist homeomorphisms of the annulus Topology. ,vol. 21, pp. 457- 467 ,(1982) , 10.1016/0040-9383(82)90023-4
V V Kozlov, Integrability and non-integrability in Hamiltonian mechanics Russian Mathematical Surveys. ,vol. 38, pp. 1- 76 ,(1983) , 10.1070/RM1983V038N01ABEH003330