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.

UDC: 514.1

Received: 01.09.2009
Revised: 18.05.2010

DOI: 10.4213/mzm8633

 English version: Mathematical Notes, 2011, 89:5, 712–725

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