Open AccessKinematical structural stability
Author(s) -
Jean Lerbet,
Noël Challamel,
François Nicot,
Félix Darve
Publication year - 2016
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2016010
Subject(s) - stability (learning theory) , duality (order theory) , divergence (linguistics) , mathematics , algebraic number , degree (music) , property (philosophy) , pure mathematics , algebra over a field , computer science , mathematical analysis , physics , epistemology , linguistics , philosophy , machine learning , acoustics
International audienceThis 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