The Symplectic Camel and Poincaré Superrecurrence: Open Problems

Poincaré’s Recurrence Theorem implies that any isolated Hamiltonian system evolving in a bounded Universe returns infinitely many times arbitrarily close to its initial phase space configuration. We discuss this and related recurrence properties from the point of view of recent advances in symplecti...

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Detalles Bibliográficos
Autor principal: de Gosson, Maurice A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513024/
https://www.ncbi.nlm.nih.gov/pubmed/33265589
http://dx.doi.org/10.3390/e20070499
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author de Gosson, Maurice A.
author_facet de Gosson, Maurice A.
author_sort de Gosson, Maurice A.
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description Poincaré’s Recurrence Theorem implies that any isolated Hamiltonian system evolving in a bounded Universe returns infinitely many times arbitrarily close to its initial phase space configuration. We discuss this and related recurrence properties from the point of view of recent advances in symplectic topology which have not yet reached the Physics community. These properties are closely related to Emergent Quantum Mechanics since they belong to a twilight zone between classical (Hamiltonian) mechanics and its quantization.
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spelling pubmed-75130242020-11-09 The Symplectic Camel and Poincaré Superrecurrence: Open Problems de Gosson, Maurice A. Entropy (Basel) Article Poincaré’s Recurrence Theorem implies that any isolated Hamiltonian system evolving in a bounded Universe returns infinitely many times arbitrarily close to its initial phase space configuration. We discuss this and related recurrence properties from the point of view of recent advances in symplectic topology which have not yet reached the Physics community. These properties are closely related to Emergent Quantum Mechanics since they belong to a twilight zone between classical (Hamiltonian) mechanics and its quantization. MDPI 2018-06-28 /pmc/articles/PMC7513024/ /pubmed/33265589 http://dx.doi.org/10.3390/e20070499 Text en © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
de Gosson, Maurice A.
The Symplectic Camel and Poincaré Superrecurrence: Open Problems
title The Symplectic Camel and Poincaré Superrecurrence: Open Problems
title_full The Symplectic Camel and Poincaré Superrecurrence: Open Problems
title_fullStr The Symplectic Camel and Poincaré Superrecurrence: Open Problems
title_full_unstemmed The Symplectic Camel and Poincaré Superrecurrence: Open Problems
title_short The Symplectic Camel and Poincaré Superrecurrence: Open Problems
title_sort symplectic camel and poincaré superrecurrence: open problems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7513024/
https://www.ncbi.nlm.nih.gov/pubmed/33265589
http://dx.doi.org/10.3390/e20070499
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