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Lyapunov exponents and chaos investi...

Bartler, Tomasz Andrzej.

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Lyapunov exponents and chaos investigation.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lyapunov exponents and chaos investigation./
Author:	Bartler, Tomasz Andrzej.
Description:	186 p.
Notes:	Source: Dissertation Abstracts International, Volume: 62-05, Section: B, page: 2391.
Contained By:	Dissertation Abstracts International62-05B.
Subject:	Engineering, Aerospace. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3014901
ISBN:	0493249583

Lyapunov exponents and chaos investigation.
Bartler, Tomasz Andrzej.

Lyapunov exponents and chaos investigation. - 186 p.

Source: Dissertation Abstracts International, Volume: 62-05, Section: B, page: 2391.

Thesis (Ph.D.)--University of Cincinnati, 1999.

This dissertation describes different methods of chaos investigation paying special attention to one of the most popular methods: Lyapunov exponents.

ISBN: 0493249583Subjects--Topical Terms:

1018395
Engineering, Aerospace.

Lyapunov exponents and chaos investigation.
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020 $a 0493249583
035 $a (UnM)AAI3014901
035 $a AAI3014901
040 $a UnM $c UnM
100 1 $a Bartler, Tomasz Andrzej. $3 1945166
245 1 0 $a Lyapunov exponents and chaos investigation.
300 $a 186 p.
500 $a Source: Dissertation Abstracts International, Volume: 62-05, Section: B, page: 2391.
500 $a Chair: David L. Richardson.
502 $a Thesis (Ph.D.)--University of Cincinnati, 1999.
520 $a This dissertation describes different methods of chaos investigation paying special attention to one of the most popular methods: Lyapunov exponents.
520 $a First a problem of Lyapunov directions and exponents of a system of ordinary differential equations with known general solutions is presented and equations describing both Lyapunov directions and exponents are derived. To verify these equations a number of simple theorems describing Lyapunov exponents of systems of linear ordinary differential equations with constant coefficients are proven.
520 $a Ordinary differential equations describing Lyapunov directions and exponents are derived and a new algorithm based on these equations is created. The new algorithm does not use reorthogonalisation (orthogonalisation is "built in" into equations describing Lyapunov directions).
520 $a A number of miscellaneous results is included. A diagonalizing transformation that can be used to compute Lyapunov exponents is presented. A number of estimates and alternative methods that can be used to compute Lyapunov exponents are also shown. Effects of differential equations stabilization are described.
520 $a A number of examples is presented through this dissertation to illustrate derived theorems and algorithms. The most common test system is a system of ordinary differential equations with constant coefficients. Also Lorenz system, Mathieu equation and Duffing's equation are used as an illustration. The most interesting application of derived methods presented in this dissertation is a three body problem (satellite motion with a Moon influence). This example shows that there are regions of phase space where orbits are chaotic.
590 $a School code: 0045.
650 4 $a Engineering, Aerospace. $3 1018395
650 4 $a Physics, General. $3 1018488
650 4 $a Mathematics. $3 515831
690 $a 0538
690 $a 0605
690 $a 0405
710 2 0 $a University of Cincinnati. $3 960309
773 0 $t Dissertation Abstracts International $g 62-05B.
790 1 0 $a Richardson, David L., $e advisor
790 $a 0045
791 $a Ph.D.
792 $a 1999
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3014901