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Perturbation theory for periodic orbits in a class of infinite dimensional Hamiltonian systems

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Abstract

We consider a class of Hamiltonian systems describing an infinite array of coupled anharmonic oscillators, and we study the bifurcation of periodic orbits off the equilibrium point. The family of orbits we construct can be parametrized by their periods which belong to Cantor sets of large measure containing certain periods of the linearized problem as accumulation points. The infinitely many holes forming a dense set on which the existence of a periodic orbit cannot be proven originate from a dense set of resonances that are present in the system. We also have a result concerning the existence of solutions of arbitrarily large amplitude.

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References

  • [AF] Albanese, C., Fröhlich, J.: Periodic Solutions ... I. Commun. Math. Phys.116, 475 (1988)

    Article  Google Scholar 

  • [AFS] Albanese, C., Fröhlich, J., Spencer, T.: Periodic Solutions ... II. Commun. Math. Phys.119, 677 (1988)

    Article  Google Scholar 

  • [FMSS] Fröhlich, J., Martinelli, F., Scoppola, E., Spencer, T.: Constructive proof of localization in the Anderson tight binding model. Commun. Math. Phys.101, 21 (1985)

    Article  Google Scholar 

  • [FS] Fröhlich, J., Spencer, T.: Absence of diffusion in the Anderson tight binding model for large disorder or low energy. Commun. Math. Phys.88, 151 (1983)

    Article  Google Scholar 

  • [SW] Simon, B., Wolff, T.: Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Commun. Pure Appl. Math.39, 75 (1985)

    Google Scholar 

  • [DLS] Delyon, F., Lévy, Y., Souillard, B.: Anderson localization for multidimensional systems at large disorder or low energy. Commun. Math. Phys.100, 463 (1985)

    Article  Google Scholar 

  • [DK] von Dreyfus, H., Klein, A.: Irvine preprint (1988)

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Author notes

  1. Claudio Albanese

    Present address: Department of Physics, Princeton University, POB 708, 08544, Princeton, NJ, USA

Authors and Affiliations

  1. Institut für Theoretische Physik, ETH-Hönggerberg, CH-8093, Zürich, Switzerland

    Claudio Albanese & Jürg Fröhlich

Authors
  1. Claudio Albanese
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  2. Jürg Fröhlich
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Communicated by A. Jaffe

Address after September 1990

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Albanese, C., Fröhlich, J. Perturbation theory for periodic orbits in a class of infinite dimensional Hamiltonian systems. Commun.Math. Phys. 138, 193–205 (1991). https://doi.org/10.1007/BF02099674

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  • DOI: https://doi.org/10.1007/BF02099674

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