Classifying orbits in the classical Henon-Heiles Hamiltonian system
Euaggelos E. Zotos
备注：
Published in Nonlinear Dynamics (NODY) journal. arXiv admin note: previous papers with related context: arXiv:1406.0446, arXiv:1404.3961, arXiv:1501.06699
发表信息：
Nonlinear Dynamics (NODY), 2015, vol. 79, pp. 1665-1677
The Hénon-Heiles potential is undoubtedly one of the most simple, classical and characteristic Hamiltonian systems. The aim of this work is to reveal the influence of the value of the total orbital energy, which is the only parameter of the system, on the different families of orbits, by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits composing the main regular families evolve when energy varies. In particular, we conduct a thorough numerical investigation distinguishing between ordered and chaotic orbits, considering only bounded motion for several energy levels. The smaller alignment index (SALI) was computed by numerically integrating the equations of motion as well as the variational equations to extensive samples of orbits in order to distinguish safely between ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics that utilizes the Fourier transform of the time series of each coordinate is used to identify the various families of regular orbits and also to recognize the secondary resonances that bifurcate from them. Our exploration takes place both in the physical $(x,y)$ and the phase $(y,\dot{y})$ space for a better understanding of the orbital properties of the system. It was found, that for low energy levels the motion is entirely regular being the box orbits the most populated family, while as the value of the energy increases chaos and several resonant families appear. We also observed, that the vast majority of the resonant orbits belong in fact in bifurcated families of the main 1:1 resonant family. We have also compared our results with previous similar outcomes obtained using different chaos indicators.
Beyond the Largest Lyapunov Exponent: Entropy-Based Diagnostics of Chaos in Henon-Heiles and N-Body Dynamics
University of Concepción（康塞普西翁大学）；National Institute for Nuclear Physics – INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；National Institute of Astrophysics - Arcetri Astrophysical Observatory (INAF-OAA)（意大利国家天体物理研究所阿切特里天文台）；National Council of Research - Institute of Complex Systems（国家研究委员会复杂系统研究所）；National Institute of Nuclear Physics (INFN) - Florence unit（意大利国家核物理研究所佛罗伦萨分部）；University of Florence（佛罗伦萨大学）
我们重新审视经典弦运动在近pp波的限制AdS $_5\times$ S $^5$。已知Toda格模型是可积的。但如果指数势在有限阶截断，则系统可能变得不可积。特别地，当三粒子周期Toda链中的指数势在动力学变量的三阶处被截断时，所得到的系统就成为一个著名的非可积系统，Henon-Heiles模型.在AdS $_5\times$ S $^5$的近pp波极限上也可能发生同样的情况，在这个极限上，经典弦运动变得混沌。
Recurrence time entropy and weak chaos in Hamiltonian flows
São Paulo State University (UNESP)（圣保罗州立大学）；Institute of Geosciences and Exact Sciences（地球科学与精确科学研究所）；University of São Paulo（圣保罗大学）；Institute of Physics（物理研究所）；State University of Ponta Grossa（蓬塔格罗萨州立大学）
