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This article is cited in 2 scientific papers (total in 2 papers)
Integrals of Motion in Time-periodic Hamiltonian Systems:
The Case of the Mathieu Equation
Athanasios C. Tzemos, George Contopoulos Research Center for Astronomy and Applied Mathematics
of the Academy of Athens,
Soranou Efessiou 4, GR-11527 Athens, Greece
Abstract:
We present an algorithm for constructing analytically approximate integrals of motion in
simple time-periodic Hamiltonians of the form $H=H_0+
\varepsilon H_i$, where $\varepsilon$ is a perturbation parameter. We apply our algorithm in a Hamiltonian system whose dynamics is governed by the Mathieu equation and examine in detail the orbits and their stroboscopic invariant curves for different values of $\varepsilon$. We find the values of $\varepsilon_{crit}$ beyond which the orbits escape to infinity and construct integrals which are expressed as series in the perturbation parameter $\varepsilon$ and converge up to $\varepsilon_{crit}$. In the absence of resonances the invariant curves are concentric ellipses which are approximated very well by our integrals. Finally, we construct an integral of motion which describes the hyperbolic stroboscopic invariant curve of a resonant case.
Keywords:
Hamiltonian systems, integrals of motion, Mathieu’s equation.
Received: 13.07.2020 Accepted: 30.11.2020
Citation:
Athanasios C. Tzemos, George Contopoulos, “Integrals of Motion in Time-periodic Hamiltonian Systems:
The Case of the Mathieu Equation”, Regul. Chaotic Dyn., 26:1 (2021), 89–104
Linking options:
https://www.mathnet.ru/eng/rcd1103 https://www.mathnet.ru/eng/rcd/v26/i1/p89
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Abstract page: | 74 | References: | 17 |
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