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INSTABILITY IN THE PRESENCE OF AN INDEFINITE CONSERVATION LAW

PETRE BIRTEA

Departamentul de Matematică, Universitatea de Vest din Timisoara, RO–1900 Timişoara, Romania

https://doi.org/10.1142/S0219887810004373Cited by:0 (Source: Crossref)

Abstract

Consider a C¹ vector field X on a finite-dimensional manifold M and x_e an equilibrium point for the dynamics . We will prove that if I is a C² constant of motion for X such that x_e is also a critical point of I, then is a constant of motion for the linearized system . As a consequence we will give an instability result under the condition that is an indefinite quadratic form. If x_e is not a critical point of I, then we obtain as a constant of motion for the linearized system.

Keywords:

AMSC: 37C10, 37C75

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