Geodesic
Invariants of the Homoclinic Trajectories of a Two-Dimensional Diffeomorphism
Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 755-770

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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, hyperbolic fixed point, separatrix
Mots-clés : monodromy matrix, homoclinic point. 
@article{MZM_2011_89_5_a9,
     author = {R. A. Mekhtiev},
     title = {Invariants of the {Homoclinic} {Trajectories} of a {Two-Dimensional} {Diffeomorphism}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {755--770},
     publisher = {mathdoc},
     volume = {89},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a9/}
}
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R. A. Mekhtiev. Invariants of the Homoclinic Trajectories of a Two-Dimensional Diffeomorphism. Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 755-770. http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a9/