| Abstract: |
| Normally hyperbolic invariant manifolds (NHIMs) are ubiquitous in Hamiltonian systems, including models from celestial mechanics. However, real-life systems are often subject to dissipative forces. Examples from celestial mechanics include tidal forces, Stokes drag, Poynting-Robertson effect, Yarkowski/YORP effects, atmospheric drag. Adding a dissipation to a Hamiltonian system is a singular perturbation that radically changes its long term behavior. In this work, we study geometric properties of NHIMs for conformally symplectic systems, which model mechanical systems with friction proportional to velocity. We show that certain conditions among rates and the conformal factor are equivalent to the NHIM being symplectic. Specifically, we show that the hyperbolicity rates for symplectic NHIMs satisfy pairing rules similar to those for Lyapunov exponents and eigenvalues of periodic orbits. |
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