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December 2008 Poincaré map in fractal analysis of spiral trajectories of planar vector fields
Darko Žubrinić, Vesna Županović
Bull. Belg. Math. Soc. Simon Stevin 15(5): 947-960 (December 2008). DOI: 10.36045/bbms/1228486418

Abstract

We study the box dimension and Minkowski content of spiral trajectories of planar vector fields, using information about the asymptotic behaviour of iterates of the Poincaré map. An auxilliary tool is a flow-sector theorem near the weak focus, which is of a similar nature as the well known flow-box theorem. Applications include Hopf bifurcation and Liénard systems. We obtain all possible values of box dimensions of spiral trajectories around weak focus, associated with polynomial vector fields.

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Darko Žubrinić. Vesna Županović. "Poincaré map in fractal analysis of spiral trajectories of planar vector fields." Bull. Belg. Math. Soc. Simon Stevin 15 (5) 947 - 960, December 2008. https://doi.org/10.36045/bbms/1228486418

Information

Published: December 2008
First available in Project Euclid: 5 December 2008

zbMATH: 1153.37011
MathSciNet: MR2484143
Digital Object Identifier: 10.36045/bbms/1228486418

Subjects:
Primary: 34C15 , 37C45 , 37G10 , 37G15

Keywords: box dimension , flow-sector , Hopf bifurcation , Liénard system , Poincaré map , spiral

Rights: Copyright © 2008 The Belgian Mathematical Society

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Vol.15 • No. 5 • December 2008
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