Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods

Arni S.R.Srinivasa Rao; Steven G. Krantz

doi:10.1007/s41745-021-00257-x

Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods

Arni S.R.Srinivasa Rao, Steven G. Krantz

Research output: Contribution to journal › Review article › peer-review

Abstract

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.

Original language	English (US)
Pages (from-to)	419-429
Number of pages	11
Journal	Journal of the Indian Institute of Science
Volume	101
Issue number	3
DOIs	https://doi.org/10.1007/s41745-021-00257-x
State	Published - Jul 2021

Keywords

Evolution
Stochastic dynamics
Topological dynamics

ASJC Scopus subject areas

General

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10.1007/s41745-021-00257-x

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@article{bc34a1c055bd47bc8337dfd139cfc266,

title = "Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods",

abstract = "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 Poincar{\'e} and Lyapunov are described. Smale{\textquoteright}s contributions are highlighted. Markovian models are considered. Semi-group actions are a tool in this study.",

keywords = "Evolution, Stochastic dynamics, Topological dynamics",

author = "Rao, {Arni S.R.Srinivasa} and Krantz, {Steven G.}",

note = "Funding Information: We thank two anonymous referees for their helpful comments during the revision process. Publisher Copyright: {\textcopyright} 2021, Indian Institute of Science.",

year = "2021",

month = jul,

doi = "10.1007/s41745-021-00257-x",

language = "English (US)",

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pages = "419--429",

journal = "Journal of the Indian Institute of Science",

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T2 - From Classical Mechanics and Astronomy to Modern Methods

AU - Rao, Arni S.R.Srinivasa

AU - Krantz, Steven G.

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - Evolution

KW - Stochastic dynamics

KW - Topological dynamics

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UR - http://www.scopus.com/inward/citedby.url?scp=85111800819&partnerID=8YFLogxK

U2 - 10.1007/s41745-021-00257-x

DO - 10.1007/s41745-021-00257-x

M3 - Review article

AN - SCOPUS:85111800819

SN - 0970-4140

VL - 101

SP - 419

EP - 429

JO - Journal of the Indian Institute of Science

JF - Journal of the Indian Institute of Science

IS - 3

ER -

Dynamical Systems: From Classical Mechanics and Astronomy to Modern Methods

Abstract

Keywords

ASJC Scopus subject areas

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