Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems

A. Raouf Chouikha

Applicationes Mathematicae (2005)

  • Volume: 32, Issue: 4, page 405-424
  • ISSN: 1233-7234

Abstract

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We are interested in conditions under which the two-dimensional autonomous system ẋ = y, ẏ = -g(x) - f(x)y, has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function in a neighborhood of 0 under certain conditions. Necessary conditions are also given. Furthermore, Raleigh systems having a monotonic (or non-monotonic) period are considered.

How to cite

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A. Raouf Chouikha. "Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems." Applicationes Mathematicae 32.4 (2005): 405-424. <http://eudml.org/doc/279839>.

@article{A2005,
abstract = { We are interested in conditions under which the two-dimensional autonomous system ẋ = y, ẏ = -g(x) - f(x)y, has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function in a neighborhood of 0 under certain conditions. Necessary conditions are also given. Furthermore, Raleigh systems having a monotonic (or non-monotonic) period are considered. },
author = {A. Raouf Chouikha},
journal = {Applicationes Mathematicae},
keywords = {Liénard system},
language = {eng},
number = {4},
pages = {405-424},
title = {Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems},
url = {http://eudml.org/doc/279839},
volume = {32},
year = {2005},
}

TY - JOUR
AU - A. Raouf Chouikha
TI - Monotonicity of the period function for some planar differential systems. Part II: Liénard and related systems
JO - Applicationes Mathematicae
PY - 2005
VL - 32
IS - 4
SP - 405
EP - 424
AB - We are interested in conditions under which the two-dimensional autonomous system ẋ = y, ẏ = -g(x) - f(x)y, has a local center with monotonic period function. When f and g are (non-odd) analytic functions, Christopher and Devlin [C-D] gave a simple necessary and sufficient condition for the period to be constant. We propose a simple proof of their result. Moreover, in the case when f and g are of class C³, the Liénard systems can have a monotonic period function in a neighborhood of 0 under certain conditions. Necessary conditions are also given. Furthermore, Raleigh systems having a monotonic (or non-monotonic) period are considered.
LA - eng
KW - Liénard system
UR - http://eudml.org/doc/279839
ER -

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