Geometric Dynamics on Riemannian Manifolds

Constantin Udriste and Ionel Tevy
Additional contact information
Constantin Udriste: Department of Mathematics-Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania
Ionel Tevy: Department of Mathematics-Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, 060042 Bucharest, Romania

Mathematics, 2020, vol. 8, issue 1, 1-14

Abstract: The purpose of this paper is threefold: (i) to highlight the second order ordinary differential equations (ODEs) as generated by flows and Riemannian metrics (decomposable single-time dynamics); (ii) to analyze the second order partial differential equations (PDEs) as generated by multi-time flows and pairs of Riemannian metrics (decomposable multi-time dynamics); (iii) to emphasise second order PDEs as generated by m -distributions and pairs of Riemannian metrics (decomposable multi-time dynamics). We detail five significant decomposed dynamics: (i) the motion of the four outer planets relative to the sun fixed by a Hamiltonian, (ii) the motion in a closed Newmann economical system fixed by a Hamiltonian, (iii) electromagnetic geometric dynamics, (iv) Bessel motion generated by a flow together with an Euclidean metric (created motion), (v) sinh-Gordon bi-time motion generated by a bi-flow and two Euclidean metrics (created motion). Our analysis is based on some least squares Lagrangians and shows that there are dynamics that can be split into flows and motions transversal to the flows.

Keywords: dynamical systems; generated ODEs and PDEs; single-time geometric dynamics; multi-time geometric dynamics; decomposable dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/1/79/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/1/79/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:1:p:79-:d:304811

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().