engleski

Fractal analysis of Hopf bifurcation at infinity

Using geometric inversion with respect to the origin, we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent definition is provided using stereographic projection on the Riemann sphere. We study its basic properties, and apply it to the study of the Hopf–Takens bifurcation at infinity. We show that for any given phase portrait $\mathcal P$ of a polynomial vector field there exists a constructive polynomial vector field such that its phase portrait is obtained from $\mathcal P$ by geometric inversion with respect to the origin.

spiral; box dimension of unbounded sets; Minkowski content; planar vector field; Hopf–Takens bifurcation at infinity

Rad je koautor G.Radunović kao predavanje prezentirao na skupu Equadiff 2011, održanom od 01.-05.08.2011., Loughborough, Engleska.