2D Generating Surfaces and Dividing Surfaces in Hamiltonian Systems with Three Degrees of Freedom
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS(2024)
摘要
In our previous work, we developed two methods for generalizing the construction of a periodic orbit dividing surface for a Hamiltonian system with three or more degrees of freedom. Starting with a periodic orbit, we extend it to form a torus or cylinder, which then becomes a higher-dimensional object within the energy surface (see [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b]). In this paper, we present two methods to construct dividing surfaces not from periodic orbits but by using 2D surfaces (2D geometrical objects) in a Hamiltonian system with three degrees of freedom. To illustrate the algorithm for this construction, we provide benchmark examples of three-degree-of-freedom Hamiltonian systems. Specifically, we employ the uncoupled and coupled cases of the quadratic normal form of a Hamiltonian system with three degrees of freedom.
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关键词
Chemical reaction dynamics,phase space,Hamiltonian system,periodic orbit,dividing surface,normally hyperbolic invariant manifold,dynamical astronomy
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