Naslov
Characteristic box dimension of Poincare map of nilpotent focus

Autori
Lana Horvat Dmitrović, Vesna Županović

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
EQUADIFF 2015 / - Lyon : Universite Claude Bernard 1, 2015, 232-232

Skup
EQUADIFF 2015

Mjesto i datum
Lyon, Francuska, 06.07.2015. - 10.07.2015

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
dynamical system; nilpotent focus; characteristic dimension

Sažetak
We show how box dimension of an orbit generated by the Poincare map or by the unit-time map, can be used in studying the cyclicity problem of nilpotent singularities of planar vector elds. On the characteristic curve of nilpotent singularity we de ne characteristic map and characteristic box dimension in order to obtain multiplicity of the singularity. In the case of Hopf-Takens bifurcation or saddle-node bifurcation, there is already known connection between the multiplicity of singularity and the box dimension of the Poincare map or unit-time map. We generalize that results for nilpotent singularities. The box dimension of the Poincare map near the nilpotent focus on the characteristic curve reveals the upper bound for cyclicity.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA