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Strong isochronicity of the Lienard system

Strong isochronicity of the Lienard system ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 5, pp. 615–618.  c Pleiades Publishing, Inc., 2006. Original Russian Text c V.V. Amel’kin, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 5, pp. 579–582. ORDINARY DIFFERENTIAL EQUATIONS V. V. Amel’kin Belarus State University, Minsk, Belarus Received June 9, 2005 DOI: 10.1134/S0012266106050016 Consider the Lienard differential equation x ¨ + B(x)˙ x + A(x)=0 (1) under the assumption that A(x)and B(x) are real holomorphic functions given by the formulas ∞ ∞ i j A(x)= x + A x and B(x)= B x ,where A and B are some constants. i j i j i=2 j=1 The Lienard equation (1), often encountered in applications, has been studied comprehensively, and is still under study, from various viewpoints. Here the passage to an equivalent planar dynam- ical system is the usual technique. One of such equivalent systems is x ˙ = −y, y˙ = A(x) − B(x)y. (2) Let π/2and 3π/2 be the polar angles of two rays l and l issuing from the origin O(0, 0) of the 1 2 Cartesian coordinate system on the phase plane xOy of system (2). Definition (cf. [1]). System (2) is strongly isochronous at the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Strong isochronicity of the Lienard system

Amel’kin, V.
Differential Equations , Volume 42 (5) – Jun 15, 2006
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References (4)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266106050016
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 5, pp. 615–618.  c Pleiades Publishing, Inc., 2006. Original Russian Text c V.V. Amel’kin, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 5, pp. 579–582. ORDINARY DIFFERENTIAL EQUATIONS V. V. Amel’kin Belarus State University, Minsk, Belarus Received June 9, 2005 DOI: 10.1134/S0012266106050016 Consider the Lienard differential equation x ¨ + B(x)˙ x + A(x)=0 (1) under the assumption that A(x)and B(x) are real holomorphic functions given by the formulas ∞ ∞ i j A(x)= x + A x and B(x)= B x ,where A and B are some constants. i j i j i=2 j=1 The Lienard equation (1), often encountered in applications, has been studied comprehensively, and is still under study, from various viewpoints. Here the passage to an equivalent planar dynam- ical system is the usual technique. One of such equivalent systems is x ˙ = −y, y˙ = A(x) − B(x)y. (2) Let π/2and 3π/2 be the polar angles of two rays l and l issuing from the origin O(0, 0) of the 1 2 Cartesian coordinate system on the phase plane xOy of system (2). Definition (cf. [1]). System (2) is strongly isochronous at the

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Differential Equations – Springer Journals

Published: Jun 15, 2006

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