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Multidimensional continued fractions, dynamic renormalization and KAM theory
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Orientador(es)
Resumo(s)
The disadvantage of ‘traditional’ multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space SL(d,Z)\ SL(d, R) (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. As an example, we explicitly construct a renormalization scheme for the linearization of vector fields on tori of arbitrary dimension..
Descrição
Palavras-chave
Fraction Algorithms Dynamics of Flows Generic Vectors KAM Theory
Contexto Educativo
Citação
Khanin, Kostya; João Lopes Dias and Jens Marklof . (2007). “Multidimensional continued fractions, dynamic renormalization and KAM theory”. Communications in Mathematical Physics , Volume 270: pp.197-231 . (Search PDF in 2023)
Editora
Springer