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On resonant hamiltonians with two degrees of freedom near an equilibrium point

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Stochastic Behavior in Classical and Quantum Hamiltonian Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 93))

Abstract

This paper discusses the flow of a classical Hamiltonian with two degrees of freedom near an equilibrium point under the assumption that its quadratic part assumes the form

$$L_ \pm = \tfrac{1}{2}(x_1^2 + y_1^2 ) \pm \tfrac{1}{2}(x_2^2 + y_2^2 ) .$$

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References

  1. Moser, J., Regularization of Kepler's problem and the averaging method on a manifold, Comm. Pure Appl. Math. 23, (1970) 609–636.

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  2. Sokol'skii, A. G., On stability of an autonomous Hamiltonian system with two degrees of freedom in the case of equal frequencies, Appl. Math. and Mech. 38 (1974) 791–799.

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  3. Kummer, M., On resonant nonlinearly coupled oscillators with two equal frequencies, Comm. Math. Phys. 48 (1976) 53–79. (The expression (35), p. 63 of Ref. [3] is only correct for n = 2, whereas the expression (2.26) of the present paper is correct for general n.)

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  4. Kummer, M., On resonant classical Hamiltonians with two equal frequencies, Comm. Math. Phys. 58 (1978) 85–112. For a more complete bibliography see References [3], [4].

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Authors and Affiliations

  1. University of Toledo, 43606, Toledo, Ohio

    Martin Kummer

Authors
  1. Martin Kummer
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Giulio Casati Joseph Ford

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© 1979 Springer-Verlag

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Kummer, M. (1979). On resonant hamiltonians with two degrees of freedom near an equilibrium point. In: Casati, G., Ford, J. (eds) Stochastic Behavior in Classical and Quantum Hamiltonian Systems. Lecture Notes in Physics, vol 93. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021738

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  • DOI: https://doi.org/10.1007/BFb0021738

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09120-2

  • Online ISBN: 978-3-540-35510-6

  • eBook Packages: Springer Book Archive

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