On the dynamics of a seventh-order generalized H\'enon-Heiles potential
| Autor: | Wei Chen, F. L. Dubeibe, Euaggelos E. Zotos |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
010302 applied physics
Chaotic Low-dimensional chaos General Physics and Astronomy Numerical simulations of chaotic systems 02 engineering and technology 021001 nanoscience & nanotechnology Critical value Nonlinear Sciences - Chaotic Dynamics 01 natural sciences lcsh:QC1-999 Nonlinear Sciences::Chaotic Dynamics Bounded function 0103 physical sciences Homogeneous space Ergodic theory Hénon-Heiles Hamiltonian Statistical physics Well-defined Mathematics - Dynamical Systems 0210 nano-technology lcsh:Physics Mathematics |
| Zdroj: | Results in Physics, Vol 18, Iss, Pp 103278-(2020) |
| Popis: | This paper deals with the derivation and analysis of a seventh-order generalization of the H\'enon-Heiles potential. The new potential has axial and reflection symmetries, and finite escape energy with three channels of escape. Based on SALI indicator and exits basins, the dynamic behavior of the seventh-order system is investigated qualitatively in cases of bounded and unbounded movement. Moreover, a quantitative analysis is carried out through the percentage of chaotic orbits and the basin entropy, respectively. After classifying large sets of initial conditions of orbits for several values of the energy constant in both regimes, we observe that when the energy moves away from the critical value, the chaoticity of the system decreases and the basin structure becomes simpler with sharper and well defined bounds. Our results suggest that when the seventh-order contributions of the potential are taken into account, the system becomes less ergodic in comparison with the classical version of the H\'enon-Heiles system. Comment: 10 pages, 7 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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