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A survey of the Hénon-Heiles Hamiltonian with applications to related examples

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Book cover Stochastic Behavior in Classical and Quantum Hamiltonian Systems

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

Abstract

This paper surveys some recent techniques and results for Hamiltonian systems in the context of the Hénon-Heiles Hamiltonian. The paper attempts to give some reasonable interpretation of various numerical (computer) results alongside recent mathematical techniques and results presented as they apply to this Hamiltonian. In particular, various computed periodic orbits are identified with geometrically constructed periodic orbits and rigorous conclusions concerning the stability status of the orbit as the energy of the system changes are indicated whenever possible. The paper concludes with a discussion of some related Hamiltonians and suggested computer experiments.

**On leave from Hunter College, C.U.N.Y.

Author's research supported in part by National Research Council of Canada, Grant A8507.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hunter College, C.U.N.Y., New York, N.Y.

    R. C. Churchill

  2. Department of Mathematics, S.U.N.Y. at Albany, Albany, N.Y.

    G. Pecelli

  3. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta

    D. L. Rod

Authors
  1. R. C. Churchill
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  2. G. Pecelli
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  3. D. L. Rod
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Giulio Casati Joseph Ford

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© 1979 Springer-Verlag

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Churchill, R.C., Pecelli, G., Rod, D.L. (1979). A survey of the Hénon-Heiles Hamiltonian with applications to related examples. 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/BFb0021739

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  • DOI: https://doi.org/10.1007/BFb0021739

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