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The Typical Dynamics of Some Mappings Determined by Piecewise Linear Functions

The Typical Dynamics of Some Mappings Determined by Piecewise Linear Functions Differential Equations, Vol. 41, No. 2, 2005, pp. 238–245. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 2, 2005, pp. 225–232. Original Russian Text Copyright c 2005 by Malets, Pilyugin. ORDINARY DIFFERENTIAL EQUATIONS The Typical Dynamics of Some Mappings Determined by Piecewise Linear Functions M. N. Malets and S. Yu. Pilyugin St. Petersburg State University, St. Petersburg, Russia Received August 3, 2004 INTRODUCTION In the present paper, we consider the class of dynamical systems induced by mappings of the Euclidean space R of the form '(v)= B(v +(v));v 2 R ; (0) where B is a nonsingular matrix and the nonlinearity  is determined by the choice of a scalar function f (x), x 2 R (for a rigorous de nition, see Section 1). Such mappings arise in the complete discretization of parabolic partial di erential equations [1, 2], and their analysis is important for the analysis of the behavior of approximate solutions of parabolic equations on unbounded time intervals. Mappings of the form (0) were considered in [1, 2] in the case of smooth functions f . In the present paper, we consider the case of piecewise linear functions f . Since a piecewise linear function f is de http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The Typical Dynamics of Some Mappings Determined by Piecewise Linear Functions

Differential Equations , Volume 41 (2) – May 16, 2005

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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2005 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/s10625-005-0154-x
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 41, No. 2, 2005, pp. 238–245. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 2, 2005, pp. 225–232. Original Russian Text Copyright c 2005 by Malets, Pilyugin. ORDINARY DIFFERENTIAL EQUATIONS The Typical Dynamics of Some Mappings Determined by Piecewise Linear Functions M. N. Malets and S. Yu. Pilyugin St. Petersburg State University, St. Petersburg, Russia Received August 3, 2004 INTRODUCTION In the present paper, we consider the class of dynamical systems induced by mappings of the Euclidean space R of the form '(v)= B(v +(v));v 2 R ; (0) where B is a nonsingular matrix and the nonlinearity  is determined by the choice of a scalar function f (x), x 2 R (for a rigorous de nition, see Section 1). Such mappings arise in the complete discretization of parabolic partial di erential equations [1, 2], and their analysis is important for the analysis of the behavior of approximate solutions of parabolic equations on unbounded time intervals. Mappings of the form (0) were considered in [1, 2] in the case of smooth functions f . In the present paper, we consider the case of piecewise linear functions f . Since a piecewise linear function f is de

Journal

Differential EquationsSpringer Journals

Published: May 16, 2005

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