A perturbation theorem for linear Hamiltonian systems with bounded orbits

Roberta Fabbri; Carmen Núñez; Ana M. Sanz

doi:10.3934/dcds.2005.13.623

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2005, Volume 13, Issue 3: 623-635. Doi: 10.3934/dcds.2005.13.623

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A perturbation theorem for linear Hamiltonian systems with bounded orbits

1.
Università di Firenze, Dipartimento di Sistemi e Informatica, Via Santa Marta 3, 50139 Firenze
2.
Universidad de Valladolid, Departamento de Matemática Aplicada, ETSII, Paseo del Cauce s/n, 47011 Valladolid
3.
Universidad de Valladolid, Departamento de Análisis Matemático y Didáctica de la Matemática, Prado de la Magdalena s/n, 47005 Valladolid

Received: July 31, 2004

Revised: January 31, 2005

Published: March 2005

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Abstract

This paper concerns the Sacker-Sell spectral decomposition of a one-parametric perturbation of a non-autonomous linear Hamiltonian system with bounded solutions. Conditions ensuring the continuous variation with respect to the parameter of the spectral intervals and subbundles are established. These conditions depend on the perturbation direction and are closely related to the topological structure of the flows induced by the initial system on the real and complex Lagrange bundles.

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Mathematics Subject Classification: Primary 37B55, 34D08; Secondary 34C11, 37D20.

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