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Transport in transitory dynamical systems. (English) Zbl 1233.37034

Authors’ abstract: We introduce the concept of a “transitory” dynamical system – one whose time-dependence is confined to a compact interval – and show how to quantify the transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case. This requires knowing only the “action” of relevant heteroclinic orbits at the intersection of invariant manifolds of “forward” and “backward” hyperbolic orbits. These manifolds can be easily computed by leveraging the autonomous nature of the vector fields on either side of the time-dependent transition. As illustrative examples we consider a two-dimensional fluid flow in a rotating double-gyre configuration and a simple one-and-a-half degree of freedom model of a resonant particle accelerator. We compare our results to those obtained using finite-time Lyapunov exponents and to adiabatic theory, discussing the benefits and limitations of each method.

MSC:

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
37D05 Dynamical systems with hyperbolic orbits and sets
37C60 Nonautonomous smooth dynamical systems
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