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Scaling in piecewise linear maps.

Kouptsov, Konstantin L.

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Scaling in piecewise linear maps.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Scaling in piecewise linear maps./
Author:	Kouptsov, Konstantin L.
Description:	78 p.
Notes:	Source: Dissertation Abstracts International, Volume: 63-12, Section: B, page: 5888.
Contained By:	Dissertation Abstracts International63-12B.
Subject:	Physics, General. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3075503
ISBN:	049395712X

Scaling in piecewise linear maps.
Kouptsov, Konstantin L.

Scaling in piecewise linear maps. - 78 p.

Source: Dissertation Abstracts International, Volume: 63-12, Section: B, page: 5888.

Thesis (Ph.D.)--New York University, 2003.

A general formalism for computed-assisted proofs for the orbit structure of certain non ergodic piecewise affine maps of the torus is developed. For a specific class of maps, it is proved that if the eigenvalues are roots of unity of degree four over the rationals (the simplest nontrivial case, comprising 8 maps), then the periodic orbits are organized into finitely many renormalizable families, with exponentially increasing period, plus a finite number of finite families. The proof is based on exact computations in algebraic number rings, where units play the role of scaling parameters. These results are applied to the analysis of propagation of round-off errors in planar rotations by certain rational angles, proving periodicity for almost all initial conditions.

ISBN: 049395712XSubjects--Topical Terms:

1018488
Physics, General.

Scaling in piecewise linear maps.
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020 $a 049395712X
035 $a (UnM)AAI3075503
035 $a AAI3075503
040 $a UnM $c UnM
100 1 $a Kouptsov, Konstantin L. $3 1926803
245 1 0 $a Scaling in piecewise linear maps.
300 $a 78 p.
500 $a Source: Dissertation Abstracts International, Volume: 63-12, Section: B, page: 5888.
500 $a Adviser: John H. Lowenstein.
502 $a Thesis (Ph.D.)--New York University, 2003.
520 $a A general formalism for computed-assisted proofs for the orbit structure of certain non ergodic piecewise affine maps of the torus is developed. For a specific class of maps, it is proved that if the eigenvalues are roots of unity of degree four over the rationals (the simplest nontrivial case, comprising 8 maps), then the periodic orbits are organized into finitely many renormalizable families, with exponentially increasing period, plus a finite number of finite families. The proof is based on exact computations in algebraic number rings, where units play the role of scaling parameters. These results are applied to the analysis of propagation of round-off errors in planar rotations by certain rational angles, proving periodicity for almost all initial conditions.
590 $a School code: 0146.
650 4 $a Physics, General. $3 1018488
650 4 $a Mathematics. $3 515831
690 $a 0605
690 $a 0405
710 2 0 $a New York University. $3 515735
773 0 $t Dissertation Abstracts International $g 63-12B.
790 1 0 $a Lowenstein, John H., $e advisor
790 $a 0146
791 $a Ph.D.
792 $a 2003
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3075503