[Transitions continues entre orbites dans un système de particules inélastique unidimensionnel]
Nous étudions les transitions continues entre différentes orbites périodiques dans un système unidimensionnel inélastique à deux particules. Nous expliquons pourquoi les transitions continues qui apparaissent lorsque l'on ajoute ou enlève une collision sont, en général, de codimension 2. Cependant, nous montrons qu'il existe un ensemble infini de transitions dégénérées de codimension 1. Nous fournissons une méthode qui, en se basant uniquement sur l'ensemble des collisions qui interviennent dans les orbites, donne un critère simple pour déterminer quelles transitions sont dégénérées.
Continuous transitions between different periodic orbits in a one-dimensional inelastic particle system with two particles are investigated. We explain why continuous transitions that occur when adding or subtracting a single collision are, generically, of co-dimension 2. However, we show that there are an infinite set of degenerate transitions of co-dimension 1. We provide an analysis that gives a simple criteria to classify which transitions are degenerated purely from the discrete set of collisions that occur in the orbits.
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@article{CRMATH_2010__348_9-10_593_0,
author = {Yang, Rong and Wylie, Jonathan J.},
title = {Continuous orbit transitions in a one-dimensional inelastic particle system},
journal = {Comptes Rendus. Math\'ematique},
pages = {593--595},
publisher = {Elsevier},
volume = {348},
number = {9-10},
year = {2010},
doi = {10.1016/j.crma.2010.04.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.04.016/}
}
TY - JOUR AU - Yang, Rong AU - Wylie, Jonathan J. TI - Continuous orbit transitions in a one-dimensional inelastic particle system JO - Comptes Rendus. Mathématique PY - 2010 SP - 593 EP - 595 VL - 348 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.04.016/ DO - 10.1016/j.crma.2010.04.016 LA - en ID - CRMATH_2010__348_9-10_593_0 ER -
%0 Journal Article %A Yang, Rong %A Wylie, Jonathan J. %T Continuous orbit transitions in a one-dimensional inelastic particle system %J Comptes Rendus. Mathématique %D 2010 %P 593-595 %V 348 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.04.016/ %R 10.1016/j.crma.2010.04.016 %G en %F CRMATH_2010__348_9-10_593_0
Yang, Rong; Wylie, Jonathan J. Continuous orbit transitions in a one-dimensional inelastic particle system. Comptes Rendus. Mathématique, Tome 348 (2010) no. 9-10, pp. 593-595. doi : 10.1016/j.crma.2010.04.016. http://www.numdam.org/articles/10.1016/j.crma.2010.04.016/
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