Invariants of the homoclinic trajectories of a two-dimensional diffeomorphism (Q650487)

Homoclinic orbits of a \(C^r\), \(r\geq 2\), map \(T:D\rightarrow D\) defined on a smooth \(2\)-dimensional manifold \(D\) are studied in this work. Various invariants for these orbits are defined and their interdependence is studied. Finally, the number of homoclinic orbits, whose distinct invariants have certain values, is estimated.