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Matematicheskie Zametki, 2011, Volume 89, Issue 5, Pages 755–770
DOI: https://doi.org/10.4213/mzm8633 (Mi mzm8633) 		 
Invariants of the Homoclinic Trajectories of a Two-Dimensional Diffeomorphism

R. A. Mekhtiev

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm8633
Abstract: We consider homoclinic trajectories under the mapping of a two-dimensional manifold onto itself, define various invariants of homoclinic trajectories, and establish relations between them. We estimate the number of homoclinic trajectories whose distinct invariants possess values within prescribed limits.
Keywords: two-dimensional diffeomorphism, homoclinic trajectory, two-dimensional manifold, monodromy matrix, hyperbolic fixed point, separatrix, homoclinic point.
Received: 01.09.2009
Revised: 18.05.2010
English version:
Mathematical Notes, 2011, Volume 89, Issue 5, Pages 712–725
DOI: https://doi.org/10.1134/S0001434611050117
Bibliographic databases:
Document Type: Article
UDC: 514.1
Language: Russian
Citation: R. A. Mekhtiev, “Invariants of the Homoclinic Trajectories of a Two-Dimensional Diffeomorphism”, Mat. Zametki, 89:5 (2011), 755–770; Math. Notes, 89:5 (2011), 712–725
Citation in format AMSBIB
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