Reduction of Dynamics with Lie Group Analysis | Zendy

Masatomo Iwasa | Zendy

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Reduction of Dynamics with Lie Group Analysis

Author(s) -

Masatomo Iwasa

Publication year - 2012

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2012/505281

Subject(s) - homogeneous space , lie group , mathematics , ordinary differential equation , lie theory , perturbation (astronomy) , singular perturbation , differential equation , reduction (mathematics) , order (exchange) , mathematical analysis , pure mathematics , adjoint representation of a lie algebra , physics , geometry , lie conformal algebra , finance , quantum mechanics , economics

This paper is mainly a review concerning singular perturbation methodsby means of Lie group analysis which has been presented by the author. We make use ofa particular type of approximate Lie symmetries in those methods in order to constructreduced systems which describe the long-time behavior of the original dynamicalsystem. Those methods can be used in analyzing not only ordinary differentialequations but also difference equations. Although this method has been mainly usedin order to derive asymptotic behavior, when we can find exact Lie symmetries, wesucceed in construction of exact solutions

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