Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the Three‐Body Problem

• Published in: Communications on pure and applied mathematics Vol. 76; no. 3; pp. 616 - 681
• Main Authors: Capiński, Maciej J., Gidea, Marian
• Format: Journal Article
• Language: English
• Published: Melbourne John Wiley & Sons Australia, Ltd 01.03.2023; John Wiley and Sons, Limited
• Subjects: Applications of mathematics; Arnold diffusion; Brownian motion; Communications systems; Diffusion; Drift; Estimates; Hamiltonian functions; Initial conditions; Orbits; Parameters; Periodic variations; Perturbation; Topology; Triton

We consider a class of autonomous Hamiltonian systems subject to small, time‐periodic perturbations. When the perturbation parameter is set to zero, the energy of the system is preserved. This is no longer the case when the perturbation parameter is non‐zero. We describe a topological method to esta...