Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods

We describe topological dynamics over a space by starting from a simple ODE emerging out of two coupled variables. We describe the dynamics of the evolution of points in space within the deterministic and stochastic frameworks. Historically dynamical systems were associated with celestial mechanics....

Descripción completa

Detalles Bibliográficos
Autores principales: Rao, Arni S. R. Srinivasa, Krantz, Steven G.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer India 2021
Materias:
Review Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8342274/
https://www.ncbi.nlm.nih.gov/pubmed/34376929
http://dx.doi.org/10.1007/s41745-021-00257-x
_version_ 1783734036945960960
author Rao, Arni S. R. Srinivasa
Krantz, Steven G.
author_facet Rao, Arni S. R. Srinivasa
Krantz, Steven G.
author_sort Rao, Arni S. R. Srinivasa
collection PubMed
description We describe topological dynamics over a space by starting from a simple ODE emerging out of two coupled variables. We describe the dynamics of the evolution of points in space within the deterministic and stochastic frameworks. Historically dynamical systems were associated with celestial mechanics. The core philosophies of two kinds of dynamics emerging from Poincaré and Lyapunov are described. Smale’s contributions are highlighted. Markovian models are considered. Semi-group actions are a tool in this study.
format Online
Article
Text
id pubmed-8342274
institution National Center for Biotechnology Information
language English
publishDate 2021
publisher Springer India
record_format MEDLINE/PubMed
spelling pubmed-83422742021-08-06 Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods Rao, Arni S. R. Srinivasa Krantz, Steven G. J Indian Inst Sci Review Article We describe topological dynamics over a space by starting from a simple ODE emerging out of two coupled variables. We describe the dynamics of the evolution of points in space within the deterministic and stochastic frameworks. Historically dynamical systems were associated with celestial mechanics. The core philosophies of two kinds of dynamics emerging from Poincaré and Lyapunov are described. Smale’s contributions are highlighted. Markovian models are considered. Semi-group actions are a tool in this study. Springer India 2021-08-06 2021 /pmc/articles/PMC8342274/ /pubmed/34376929 http://dx.doi.org/10.1007/s41745-021-00257-x Text en © Indian Institute of Science 2021 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Review Article
Rao, Arni S. R. Srinivasa
Krantz, Steven G.
Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods
title Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods
title_full Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods
title_fullStr Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods
title_full_unstemmed Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods
title_short Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods
title_sort dynamical systems: from classical mechanics and astronomy to modern methods
topic Review Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8342274/
https://www.ncbi.nlm.nih.gov/pubmed/34376929
http://dx.doi.org/10.1007/s41745-021-00257-x
work_keys_str_mv AT raoarnisrsrinivasa dynamicalsystemsfromclassicalmechanicsandastronomytomodernmethods
AT krantzsteveng dynamicalsystemsfromclassicalmechanicsandastronomytomodernmethods

Ejemplares similares