Transport, flux and growth of homoclinic Floer homology (Q445225)

The author considers homoclinic points of a compactly supported Hamiltonian diffeomorphism on the cotangent bundle of the circle. The aim of this article is to generalize to this context the Morse-Floer type homology introduced by the author in [``Homoclinic points and Floer homology'', J. Symplectic Geom. (to appear); ``Floer homology and homoclinic dynamics'' (submitted), \url{http://sma.epfl.ch/~hohloch/Floer_homology_and_homoclinic_dynamics.pdf}] which counts certain discs enclosed by segments of (un-)stable manifolds of homoclinic points on \(\mathbb R^2\). In order to include non-contractible homoclinic points, the author introduces the notion of action. Its relation to the area-preserving dynamics, such as the behaviour under iterations, is studied in detail.