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T. Eirola, S. Pilyugin (1996)
Pseudotrajectories generated by a discretization of a parabolic equationJournal of Dynamics and Differential Equations, 8
W. Oliva, Nelson Kuhl, L. Magalhaes (1993)
Diffeomorphisms of $\Bbb R^n$ with oscillatory jacobiansPublicacions Matematiques, 37
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
Differential Equations – Springer Journals
Published: May 16, 2005
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