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On resonant non linearly coupled oscillators with two equal frequencies (1976)

Kummer, Martin

Springer

Communications in mathematical physics 48 (1976), S. 53-79

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract This paper contains a detailed study of the flow that the classical Hamiltonian $$H = \tfrac{1}{2}(x\begin{array}{*{20}c} 2 \\ 1 \\ \end{array} + y\begin{array}{*{20}c} 2 \\ 1 \\ \end{array} ) + \tfrac{1}{2}(x\begin{array}{*{20}c} 2 \\ 2 \\ \end{array} + y\begin{array}{*{20}c} 2 \\ 2 \\ \end{array} ) + \mathcal{O}_3 $$ induces inR 4, $$\mathcal{O}_3 $$ representing a convergent power series that begins with a third order term. In particular the existence and stability of periodic orbits is investigated.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01609411

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