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Global surfaces of section in non-regular convex energy levels of Hamiltonian systems

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Abstract

In this paper we prove the existence of global sections of disk-type in non-regular and strictly convex energy levels of integrable and near-integrable Hamiltonian systems with two degrees of freedom. This extends a result of (Hofer et al. in Ann. Math.(2) 148(1):197–289, 1998) where the same statement is true provided the energy level is regular.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, Cidade Universitária, São Paulo, 05508-090, SP, Brazil

    C. Grotta-Ragazzo & Pedro A. S. Salomão

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  1. C. Grotta-Ragazzo
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  2. Pedro A. S. Salomão
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Correspondence to Pedro A. S. Salomão.

Additional information

C. Grotta-Ragazzo was partially supported by CNPq (Brazil) grant n. 301817/96-0. Pedro A. S. Salomão was partially supported by FAPESP (Brazil) grant n. 03/03572-3.

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Grotta-Ragazzo, C., Salomão, P.A.S. Global surfaces of section in non-regular convex energy levels of Hamiltonian systems. Math. Z. 255, 323–334 (2007). https://doi.org/10.1007/s00209-006-0026-y

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  • DOI: https://doi.org/10.1007/s00209-006-0026-y

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