Jumps of Energy Near a Homoclinic Set of a Slowly Time Dependent Hamiltonian System
| Autor: | Sergey Bolotin |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
010102 general mathematics Mathematical analysis Chaotic Degrees of freedom (statistics) 01 natural sciences Hamiltonian system 010101 applied mathematics Mathematics (miscellaneous) Adiabatic invariant Homoclinic orbit Growth rate 0101 mathematics Energy (signal processing) Hyperbolic equilibrium point |
| Zdroj: | Regular and Chaotic Dynamics. 24:682-703 |
| ISSN: | 1468-4845 1560-3547 |
| Popis: | We consider a Hamiltonian system depending on a parameter which slowly changes with rate e ≪ 1. If trajectories of the frozen autonomous system are periodic, then the system has adiabatic invariant which changes much slower than energy. For a system with 1 degree of freedom and a figure 8 separatrix, Anatoly Neishtadt [18] showed that for trajectories crossing the separatrix, the adiabatic invariant, and hence the energy, have quasirandom jumps of order e. We prove a partial analog of Neishtadt’s result for a system with n degrees of freedom such that the frozen system has a hyperbolic equilibrium possessing several homoclinic orbits. We construct trajectories staying near the homoclinic set with energy having jumps of order e at time intervals of order ∣ln e∣, so the energy may grow with rate e/∣ln e∣. Away from the homoclinic set faster energy growth is possible: if the frozen system has chaotic behavior, Gelfreich and Turaev [16] constructed trajectories with energy growth rate of order e. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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