## Wednesday July 27/8:00

MS32/Harbor 1

# Multi-Bump Homoclinic Orbits

The minisymposium will focus on the new field of multi-bump homoclinic orbits obtainable by the Melnikov method. These orbits make several fast excursions away from a given set of regular or slow motions before asymptoting to an equilibrium or a limit cycle on this set, in both forward and backward time. The fast excursions can usually be associated with an appropriate set of symbol sequences, and may form complicated fractal structures. Some types of multi-bump homoclinic orbits arise in singularly perturbed problems, in which the fast excursions are heteroclinic orbits of the inner equations, and in which these excursions are interspersed with slow segments that are solutions of the outer equations. Other types consist of several consecutive heteroclinic orbits of the inner equations. Tools used to describe multi-bump homoclinic orbits include the Melnikov method, the invariant manifold theory, rescaling, and geometric singular perturbation theory.
**Organizer: Gregor Kovacic
Rensselaer Polytechnic Institute**
*8:00:* **Multiple Homoclinic Excursions in a Neighbourhood of a non-Hamiltonian Saddle-Center**
Roberto A. Camassa, Los Alamos National Laboratory
*8:30:* **Multi-Pulse Homoclinic Orbits and Homoclinic Trees in Resonant Systems**
Gy”rgy Haller, Brown University, and Courant Institute of Mathematical Sciences, New York University
*9:00:* **Tracking Invariant Manifolds**
Tasso J. Kaper, Boston University
*9:30:* **Multi-Bump Orbits Homoclinic to Resonance Bands**
Gregor Kovacic, Organizer