Poincaré map in fractal analysis of spiral trajectories of planar vector fields
Žubrinić, Darko ; Županović, Vesna
Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, p. 947-960 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2008-11-15
Classification:  Poincaré map,  spiral,  box dimension,  flow-sector,  Hopf bifurcation,  Liénard system,  37C45,  37G10,  37G15,  34C15 
@article{1228486418,
     author = {\v Zubrini\'c, Darko and \v Zupanovi\'c, Vesna},
     title = {Poincar\'e map in fractal analysis of spiral trajectories of planar vector fields},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 947-960},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1228486418}
}

Žubrinić, Darko; Županović, Vesna. Poincaré map in fractal analysis of spiral trajectories of planar vector fields. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp.  947-960. http://gdmltest.u-ga.fr/item/1228486418/