Contact Dynamics: Legendrian and Lagrangian Submanifolds

We are proposing Tulczyjew’s triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse families, are generalized to the contact framework. These geometries permit us to determine so-called generating family (...

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Autores principales:	Oğul Esen, Manuel Lainz Valcázar, Manuel de León, Juan Carlos Marrero
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Tulczyjew’s triple contact dynamics evolution contact dynamics Legendrian submanifold Lagrangian submanifold Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/eda3043d3612424c80d47ab12514132e
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id	oai:doaj.org-article:eda3043d3612424c80d47ab12514132e
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spelling	oai:doaj.org-article:eda3043d3612424c80d47ab12514132e2021-11-11T18:15:53ZContact Dynamics: Legendrian and Lagrangian Submanifolds10.3390/math92127042227-7390https://doaj.org/article/eda3043d3612424c80d47ab12514132e2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2704https://doaj.org/toc/2227-7390We are proposing Tulczyjew’s triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse families, are generalized to the contact framework. These geometries permit us to determine so-called generating family (obtained by merging a special contact manifold and a Morse family) for a Legendrian submanifold. Contact Hamiltonian and Lagrangian Dynamics are recast as Legendrian submanifolds of the tangent contact manifold. In this picture, the Legendre transformation is determined to be a passage between two different generators of the same Legendrian submanifold. A variant of contact Tulczyjew’s triple is constructed for evolution contact dynamics.Oğul EsenManuel Lainz ValcázarManuel de LeónJuan Carlos MarreroMDPI AGarticleTulczyjew’s triplecontact dynamicsevolution contact dynamicsLegendrian submanifoldLagrangian submanifoldMathematicsQA1-939ENMathematics, Vol 9, Iss 2704, p 2704 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Tulczyjew’s triple contact dynamics evolution contact dynamics Legendrian submanifold Lagrangian submanifold Mathematics QA1-939
spellingShingle	Tulczyjew’s triple contact dynamics evolution contact dynamics Legendrian submanifold Lagrangian submanifold Mathematics QA1-939 Oğul Esen Manuel Lainz Valcázar Manuel de León Juan Carlos Marrero Contact Dynamics: Legendrian and Lagrangian Submanifolds
description	We are proposing Tulczyjew’s triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse families, are generalized to the contact framework. These geometries permit us to determine so-called generating family (obtained by merging a special contact manifold and a Morse family) for a Legendrian submanifold. Contact Hamiltonian and Lagrangian Dynamics are recast as Legendrian submanifolds of the tangent contact manifold. In this picture, the Legendre transformation is determined to be a passage between two different generators of the same Legendrian submanifold. A variant of contact Tulczyjew’s triple is constructed for evolution contact dynamics.
format	article
author	Oğul Esen Manuel Lainz Valcázar Manuel de León Juan Carlos Marrero
author_facet	Oğul Esen Manuel Lainz Valcázar Manuel de León Juan Carlos Marrero
author_sort	Oğul Esen
title	Contact Dynamics: Legendrian and Lagrangian Submanifolds
title_short	Contact Dynamics: Legendrian and Lagrangian Submanifolds
title_full	Contact Dynamics: Legendrian and Lagrangian Submanifolds
title_fullStr	Contact Dynamics: Legendrian and Lagrangian Submanifolds
title_full_unstemmed	Contact Dynamics: Legendrian and Lagrangian Submanifolds
title_sort	contact dynamics: legendrian and lagrangian submanifolds
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/eda3043d3612424c80d47ab12514132e
work_keys_str_mv	AT ogulesen contactdynamicslegendrianandlagrangiansubmanifolds AT manuellainzvalcazar contactdynamicslegendrianandlagrangiansubmanifolds AT manueldeleon contactdynamicslegendrianandlagrangiansubmanifolds AT juancarlosmarrero contactdynamicslegendrianandlagrangiansubmanifolds
_version_	1718431917751140352

Contact Dynamics: Legendrian and Lagrangian Submanifolds

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