Symplectification of truncated maps for Hamiltonian systems

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Symplectification of truncated maps for Hamiltonian systems. / Andrianov, Serge.

In: Mathematics and Computers in Simulation, Vol. 57, No. 3-5, 29.08.2001, p. 139-145.

Research output: Contribution to journal › Article › peer-review

Author

Andrianov, Serge. / Symplectification of truncated maps for Hamiltonian systems. In: Mathematics and Computers in Simulation. 2001 ; Vol. 57, No. 3-5. pp. 139-145.

BibTeX

@article{8ef0d1aa09024f21bb41ef31bf2f94ab,

title = "Symplectification of truncated maps for Hamiltonian systems",

abstract = "The time-displacement operator for Hamiltonian dynamical systems M(t|t0) is a symplectic transformation - Lie map. Any truncated Lie map (Lie approximant) loses the very important symplectic property. In this report a method of correcting the truncated map is given. The matrix representation for desired symplectic map is calculated in the symbolic form. The symplectification conditions have the form of simple linear algebraic equations. The symbolic solutions of these equations are computed in advance and are stored in a database. This approach allows us to simplify the calculation process for the evolution of dynamical systems, in particular, for long time evolution.",

keywords = "Computer algebra, Exact symplectic conditions, Hamiltonian maps, Lie algebraic methods, Symplectic maps",

author = "Serge Andrianov",

year = "2001",

month = aug,

day = "29",

doi = "10.1016/S0378-4754(01)00333-0",

language = "English",

volume = "57",

pages = "139--145",

journal = "Mathematics and Computers in Simulation",

issn = "0378-4754",

publisher = "Elsevier",

number = "3-5",

}

RIS

TY - JOUR

T1 - Symplectification of truncated maps for Hamiltonian systems

AU - Andrianov, Serge

PY - 2001/8/29

Y1 - 2001/8/29

N2 - The time-displacement operator for Hamiltonian dynamical systems M(t|t0) is a symplectic transformation - Lie map. Any truncated Lie map (Lie approximant) loses the very important symplectic property. In this report a method of correcting the truncated map is given. The matrix representation for desired symplectic map is calculated in the symbolic form. The symplectification conditions have the form of simple linear algebraic equations. The symbolic solutions of these equations are computed in advance and are stored in a database. This approach allows us to simplify the calculation process for the evolution of dynamical systems, in particular, for long time evolution.

AB - The time-displacement operator for Hamiltonian dynamical systems M(t|t0) is a symplectic transformation - Lie map. Any truncated Lie map (Lie approximant) loses the very important symplectic property. In this report a method of correcting the truncated map is given. The matrix representation for desired symplectic map is calculated in the symbolic form. The symplectification conditions have the form of simple linear algebraic equations. The symbolic solutions of these equations are computed in advance and are stored in a database. This approach allows us to simplify the calculation process for the evolution of dynamical systems, in particular, for long time evolution.

KW - Computer algebra

KW - Exact symplectic conditions

KW - Hamiltonian maps

KW - Lie algebraic methods

KW - Symplectic maps

UR - http://www.scopus.com/inward/record.url?scp=0034889696&partnerID=8YFLogxK

U2 - 10.1016/S0378-4754(01)00333-0

DO - 10.1016/S0378-4754(01)00333-0

M3 - Article

AN - SCOPUS:0034889696

VL - 57

SP - 139

EP - 145

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

IS - 3-5

ER -

ID: 51672707