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Symmetry
Special Issues
Contact Geometry: Reduction, Symmetries and Applications
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Contact Geometry: Reduction, Symmetries and Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 2008

Special Issue Editor

Dr. Cristina Sardon

E-Mail Website
Guest Editor
Department of Applied Mathematics, Universidad Politécnica de Madrid, ETSII, Calle José Gutiérrez Abascal, 2, 28006 Madrid, Spain
Interests: geometric mechanics; contact structures; dissipation; discrete mechanics; discrete contact structures; discrete Hamilton—Jacobi theory; evolutionary dynamics; time-dependent dynamics; parameter dependent dynamics; conserved quantities and integrals of motion in contact mechanics; reduction by symmetry; numerical methods for contact structures; cosymplectic structures; cosymplectic numerical methods; numerical integration in geometric mechanics; physical applications of contact mechanics; nonequilibrium thermodynamics; dynamics of parachute-lie devices

Special Issue Information

Dear Colleagues,

This Special Issue is concerned with contact geometry and its role in mechanics. The intent is to gather new results on the integrability of dynamical systems that are compatible with a contact structure, through symmetry, reduction, and integration. This Special Issue will gather contributions on the continuous and discrete formalism of contact geometry, as well as classical and quantum frameworks. Another important feature of this issue is that it is focused on theoretical results with applications of such contact structures, ranging from thermodynamics to any kind of dynamical evolution. In the scope of this Special Issue is also the development of numerical integrators for contact structures and other explicitly time-dependent or parameter-dependent geometries.

We are soliciting contributions (research and review articles) covering a broad range of topics on contact geometry and reduction in, dissipation, symmetry, and integration of such contact structures, including (not limited to):

  • Design of numerical integrators preserving contact structures;
  • New results on related geometric structures, such as cosymplectic structures and their numerical integration;
  • Dissipated quantities, symmetries, and reduction in contact structures;
  • Dynamics on odd-dimensional manifolds;
  • Hamilton—Jacobi theory for time-dependent systems;
  • The role of contact structures in quantum backgrounds;
  • Dissipation and symmetry in discrete contact structures;
  • New applications of contact structures and their related geometries;
  • Generalization of symplectic dynamics to odd-dimensional dynamical systems.

Dr. Cristina Sardon
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • contact structures
  • quantum and discrete contact geometry
  • integrability through reduction of contact structures
  • conserved quantities, dissipated quantities and symmetry in contact structure

Published Papers (2 papers)

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Research

12 pages, 763 KiB  
Article
Osculating Type Ruled Surfaces with Type-2 Bishop Frame in E3
by Özgür Boyacıoğlu Kalkan and Süleyman Şenyurt
Symmetry 2024, 16(4), 498; https://doi.org/10.3390/sym16040498 - 19 Apr 2024
Viewed by 263
Abstract
The aim of this work is to investigate osculating type ruled surfaces with a type 2-Bishop frame in E3. We accomplish this by employing the symmetry of osculating curves. We examine osculating type ruled surfaces by taking into account the curvatures [...] Read more.
The aim of this work is to investigate osculating type ruled surfaces with a type 2-Bishop frame in E3. We accomplish this by employing the symmetry of osculating curves. We examine osculating type ruled surfaces by taking into account the curvatures of the base curve. We investigate the geometric properties of these surfaces, focusing on their cylindrical and developable characteristics. Moreover, we calculate the Gaussian and mean curvatures and provide the requirements for the surface to be flat and minimal. We determine the requirements for the curves lying on this surface to be geodesic, asymptotic curves, or lines of curvature. Furthermore, relations between osculating type ruled surfaces with central tangent and central normal vectors are given. Finally, some examples of these surfaces are presented. Full article
(This article belongs to the Special Issue Contact Geometry: Reduction, Symmetries and Applications)
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23 pages, 391 KiB  
Article
Time-Dependent Hamiltonian Mechanics on a Locally Conformal Symplectic Manifold
by Marcin Zając, Cristina Sardón and Orlando Ragnisco
Symmetry 2023, 15(4), 843; https://doi.org/10.3390/sym15040843 - 01 Apr 2023
Cited by 2 | Viewed by 1055
Abstract
In this paper we aim at presenting a concise but also comprehensive study of time-dependent (t-dependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We present a generalized geometric theory of canonical transformations in order to formulate an explicitly time-dependent [...] Read more.
In this paper we aim at presenting a concise but also comprehensive study of time-dependent (t-dependent) Hamiltonian dynamics on a locally conformal symplectic (lcs) manifold. We present a generalized geometric theory of canonical transformations in order to formulate an explicitly time-dependent geometric Hamilton-Jacobi theory on lcs manifolds, extending our previous work with no explicit time-dependence. In contrast to previous papers concerning locally conformal symplectic manifolds, the introduction of the time dependency that this paper presents, brings out interesting geometric properties, as it is the case of contact geometry in locally symplectic patches. To conclude, we show examples of the applications of our formalism, in particular, we present systems of differential equations with time-dependent parameters, which admit different physical interpretations as we shall point out. Full article
(This article belongs to the Special Issue Contact Geometry: Reduction, Symmetries and Applications)
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