Руслан Мехтиев
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.
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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.
Key concepts: Homoclinic orbit, Diffeomorphism, Mathematics, Manifold (fluid mechanics), Pure mathematics, Homoclinic bifurcation, Mathematical analysis, Bifurcation