Reversibility and Poincare recurrence in linear dynamical systems.

In this paper, we study the Poincare recurrence phenomenon for linear dynamical systems, that is, linear systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear dynamical systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear dynamical systems. In addition, we show that in the case of linear systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a dynamical system. Finally, we introduce the notion of output reversibility and show that in the case of linear systems, Poincare recurrence is a sufficient condition for output reversibility.

Main Author: Nersesov, Sergey.
Other Authors: Haddad, Wassim.
Language: English
Published: 2008
Online Access: http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:178331
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dc_source_str_mv IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 53, NO. 9, OCTOBER 2008
author Nersesov, Sergey.
author_facet_str_mv Nersesov, Sergey.
Haddad, Wassim.
author_or_contributor_facet_str_mv Nersesov, Sergey.
Haddad, Wassim.
author_s Nersesov, Sergey.
spellingShingle Nersesov, Sergey.
Reversibility and Poincare recurrence in linear dynamical systems.
author-letter Nersesov, Sergey.
author_sort_str Nersesov, Sergey.
author2 Haddad, Wassim.
author2Str Haddad, Wassim.
dc_title_str Reversibility and Poincare recurrence in linear dynamical systems.
title Reversibility and Poincare recurrence in linear dynamical systems.
title_short Reversibility and Poincare recurrence in linear dynamical systems.
title_full Reversibility and Poincare recurrence in linear dynamical systems.
title_fullStr Reversibility and Poincare recurrence in linear dynamical systems.
title_full_unstemmed Reversibility and Poincare recurrence in linear dynamical systems.
collection_title_sort_str reversibility and poincare recurrence in linear dynamical systems.
title_sort reversibility and poincare recurrence in linear dynamical systems.
description In this paper, we study the Poincare recurrence phenomenon for linear dynamical systems, that is, linear systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear dynamical systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear dynamical systems. In addition, we show that in the case of linear systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a dynamical system. Finally, we introduce the notion of output reversibility and show that in the case of linear systems, Poincare recurrence is a sufficient condition for output reversibility.
publishDate 2008
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dc.title Reversibility and Poincare recurrence in linear dynamical systems.
dc.creator Nersesov, Sergey.
Haddad, Wassim.
dc.description In this paper, we study the Poincare recurrence phenomenon for linear dynamical systems, that is, linear systems whose trajectories return infinitely often to neighborhoods of their initial condition. Specifically, we provide several equivalent notions of Poincare recurrence and review sufficient conditions for nonlinear dynamical systems that ensure that the system exhibits Poincare recurrence. Furthermore, we establish necessary and sufficient conditions for Poincare recurrence in linear dynamical systems. In addition, we show that in the case of linear systems the absence of volume-preservation is equivalent to the absence of Poincare recurrence implying irreversibility of a dynamical system. Finally, we introduce the notion of output reversibility and show that in the case of linear systems, Poincare recurrence is a sufficient condition for output reversibility.
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