2013/03/21 by Maxim Arnold, Arnold, Maxim, Vadim Zharnitsky +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #37J25 #Advanced Differential Equations and Dynamical Systems #Control and Stability of Dynamical Systems #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #math-ph #math.MP #msc:37J25
paper · pdf · doi:10.48550/arxiv.1303.5510
23 pages, 4 figures
openalex publication_date 2013/03/21 · arxiv created 2013/06/11 · arxiv updated 2013/06/12 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28
A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a canonical model for the study of bounded and unbounded behavior in discontinuous area-preserving mappings due to nonlinear resonances. This paper provides a general description of the map and points out its connection with another map considered earlier by Kesten. In one special case, an unbounded orbit is explicitly constructed.