In this work we give a constructive argument to establish existence of a smooth singular value decomposition (SVD) for a $C^k$ function X in the Lorentz group. We rely on the explicit structure of the polar factorization of X in order to justify the form of the SVD. Our construction gives a simple algorithm to 5nd the SVD of X , which we have used to approximate the Lyapunov exponents of a di6erential system whose fundamental matrix solution evolves on the Lorentz group. Algorithmic details and examples are given.

Smooth SVD on the Lorentz group with applications to computations of Lyapunov exponents

ELIA, CINZIA;LOPEZ, Luciano
2004-01-01

Abstract

In this work we give a constructive argument to establish existence of a smooth singular value decomposition (SVD) for a $C^k$ function X in the Lorentz group. We rely on the explicit structure of the polar factorization of X in order to justify the form of the SVD. Our construction gives a simple algorithm to 5nd the SVD of X , which we have used to approximate the Lyapunov exponents of a di6erential system whose fundamental matrix solution evolves on the Lorentz group. Algorithmic details and examples are given.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/128256
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