Bazzani Armando, Capoani Federico, Giovannozzi Massimo
Physics and Astronomy Department, Bologna University and INFN-Bologna, V. Irnerio 46, 40126 Bologna - Italy.
Physics and Astronomy Department, Bologna University, V. Irnerio 46, 40126 Bologna, Italy and Beams Department, CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland.
Phys Rev E. 2022 Sep;106(3-1):034204. doi: 10.1103/PhysRevE.106.034204.
In this paper, results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps and Hamiltonians with a time-dependent exciter are presented and discussed in detail. The applicability of the results about trapping efficiency for Hamiltonian systems to the maps considered is proven by using perturbation theory. This makes possible to determine explicit scaling laws for the trapping properties. These findings represent a generalization of previous results obtained for the case of quasi-integrable maps with parametric modulation, as well as an extension of the work by Neishtadt et al. [Regul. Chaotic Dyn. 18, 686 (2013)10.1134/S1560354713060087] on a restricted class of quasi-integrable systems with time-dependent exciters.
本文给出并详细讨论了一类具有含时激励器的拟可积映射和哈密顿量的绝热捕获到共振现象的相关结果。利用微扰理论证明了哈密顿系统中关于捕获效率的结果对所考虑的映射的适用性。这使得确定捕获特性的显式标度律成为可能。这些发现是对具有参数调制的拟可积映射情形下先前结果的推广，也是对Neishtadt等人[《规则与混沌动力学》18, 686 (2013)10.1134/S1560354713060087]关于一类具有含时激励器的受限拟可积系统工作的扩展。
