Escapes in Hamiltonian systems with multiple exit channels: part II

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• 作者：Euaggelos E. Zotos
• 关键词：Hamiltonian systems ; Harmonic oscillators ; Numerical simulations ; Escapes ; Fractals
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：82
• 期：1-2
• 页码：357-398
• 全文大小：24,998 KB
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• 作者单位：Euaggelos E. Zotos (1)
  
  1. Department of Physics, School of Science, Aristotle University of Thessaloniki, 541 24, Thessalon铆ki, Greece
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

We explore the escape dynamics in open Hamiltonian systems with multiple channels of escape continuing the work initiated in Part I. A thorough numerical investigation is conducted distinguishing between trapped (ordered and chaotic) and escaping orbits. The determination of the location of the basins of escape toward the different escape channels and their correlations with the corresponding escape periods of the orbits is undoubtedly an issue of paramount importance. We consider four different cases depending on the perturbation function which controls the number of escape channels on the configuration space. In every case, we computed extensive samples of orbits in both the configuration and the phase space by numerically integrating the equations of motion as well as the variational equations. It was found that in all examined cases, regions of non-escaping motion coexist with several basins of escape. The larger escape periods have been measured for orbits with initial conditions in the vicinity of the fractal structure, while the lowest escape rates belong to orbits with initial conditions inside the basins of escape. In addition, we related the model potential with applications in the field of reactive multichannel scattering. We hope that our numerical analysis will be useful for a further understanding of the escape mechanism of orbits in open Hamiltonian systems with two degrees of freedom. Keywords Hamiltonian systems Harmonic oscillators Numerical simulations Escapes Fractals