Kinematical structural stability

Jean  Lerbet; Noël  Challamel; François  Nicot; Félix Darve

doi:10.3934/dcdss.2016010

Article Contents

2016, Volume 9, Issue 2: 529-536. Doi: 10.3934/dcdss.2016010

This issue Previous Article On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction Next Article Analysis of an iterative scheme of fractional steps type associated to the nonlinear phase-field equation with non-homogeneous dynamic boundary conditions

Kinematical structural stability

1.
IBISC, UFRST-UEVE, 40, rue du Pelvoux CE 1455 Courcouronnes, 91020 Evry Cedex
2.
South Britain University, LIMATB -UBS -Lorient Research Center, Rue de Saint Maudé - BP 92116, 56321 Lorient cedex

Received: October 31, 2014

Revised: October 31, 2015

Published: March 2016

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Abstract

This paper gives an overview of our results obtained from 2009 until 2014 about paradoxical stability properties of non conservative systems which lead to the concept of Kinematical Structural Stability (Ki.s.s.). Due to Fischer-Courant results, this ki.s.s. is universal for conservative systems whereas new interesting situations may arise for non conservative ones. A remarkable algebraic property of the symmetric part of linear operators may generalize this result for divergence stability but leading only to a conditional ki.s.s. By duality, the concept of geometric degree of nonconservativity is highlighting. Paradigmatic examples of Ziegler systems illustrate the general results and their effectiveness.

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Mathematics Subject Classification: Primary: 34D30, 37C20; Secondary: 47A20.

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