Abstract: Hamiltonian impact systems are dynamical systems in which there are two main mechanisms which dictate the system’s behavior - Hamilton’s equations which govern the motion inside the impact system domain, and the billiard reflection rule which governs the motion upon reaching the domain boundary. As the dynamics in impact systems are piecewise smooth by nature due to the collisions with the boundary, many of the traditional tools used in the analysis of Hamiltonian systems cannot be applied to impact systems in a straightforward manner. This talk will present a class of 2 degrees-of-freedom integrable, separable, Hamiltonian impact systems whose amenability to analysis is derived from a relation between the impact structure and underlying symmetries in the Hamiltonian dynamics. By investigating different projections of the conditions for impact into phase space, we develop tools for the initial classification and analysis of the different types of dynamics in the system. In particular, under several types of perturbations, near integrable behavior is exhibited in large portions of phase space and stability results can be formulated. Applying these methodologies to additional classes of systems reveals the similarities and differences in their global phase space structure. Joint work with Vered Rom-Kedar. The talk will not assume prior knowledge of Hamiltonian systems.
Wed, 06/06/2018 - 12:00 to 13:00
Ross Building, Room 70