Exponentially long time stability near an equilibrium point for non-linearizable analytic vector fields

Timoteo Carletti

Exponentially long time stability near an equilibrium point for non-linearizable analytic vector fields

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Abstract

We study the orbit behaviour of a germ of an analytic vector field of (C^n, 0), n ≥ 2. We prove that if its linear part is semisimple, non'resonant and verifies a Bruno'like condition, then the origin is effectively stable: stable for finite but exponentially long times.

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Zeitschrift für angewandte Mathematik und Physik ZAMP
Volume	56
Publication status	Published - 2005

Keywords

Gevrey class
Bruno condition
linearization vector field
Nekhoroshev theorem.
effective stability

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abstract = "We study the orbit behaviour of a germ of an analytic vector field of (C^n, 0), n ≥ 2. We prove that if its linear part is semisimple, non'resonant and verifies a Bruno'like condition, then the origin is effectively stable: stable for finite but exponentially long times.",

keywords = " Gevrey class, Bruno condition, linearization vector field, Nekhoroshev theorem., effective stability",

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AB - We study the orbit behaviour of a germ of an analytic vector field of (C^n, 0), n ≥ 2. We prove that if its linear part is semisimple, non'resonant and verifies a Bruno'like condition, then the origin is effectively stable: stable for finite but exponentially long times.

KW - Gevrey class

KW - Bruno condition

KW - linearization vector field

KW - Nekhoroshev theorem.

KW - effective stability

M3 - Article

VL - 56

SP - 1

EP - 13

JO - Zeitschrift für angewandte Mathematik und Physik ZAMP

JF - Zeitschrift für angewandte Mathematik und Physik ZAMP

ER -

Exponentially long time stability near an equilibrium point for non-linearizable analytic vector fields

Abstract

Keywords

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