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Mat. Zametki, 2011, Volume 89, Issue 5, Pages 755–770 (Mi mz8633)  

Invariants of the Homoclinic Trajectories of a Two-Dimensional Diffeomorphism

R. A. Mekhtiev

M. V. Lomonosov Moscow State University

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

DOI: https://doi.org/10.4213/mzm8633

Full text: PDF file (574 kB)
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English version:
Mathematical Notes, 2011, 89:5, 712–725

Bibliographic databases:

UDC: 514.1
Received: 01.09.2009
Revised: 18.05.2010

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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\paper Invariants of the Homoclinic Trajectories of a Two-Dimensional Diffeomorphism
\jour Mat. Zametki
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\issue 5
\pages 755--770
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\pages 712--725
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