Naslov
Fractal Analysis of unit-time map and cyclicity of nilpotent singularities of planar vector fields

Autori
Horvat Dmitrović, Lana ; Županović, Vesna

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

Skup
10th AIMS International Conference on Dynamical Systems, Differential Equations and Applications

Mjesto i datum
Madrid, Španjolska, 07.07.2014. - 11.07.2014

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
unit-time map; box dimension; nilpotent singularity; cyclicity; node; focus

Sažetak
This article shows how fractal analysis of the unit-time map can be used in studying the cyclicity problem of nilpotent singularities. We study fractal properties such as box dimension and epsilon-neighbourhood of discrete orbits generated by the unit-time map. In the case of bifurcations of non-hyperbolic singularities such as saddle-node or Hopf-Takens bifurcation, there is already known connection between the multiplicity of singularity and the box dimension of the unit-time map or Poincare map. In this article we study how the box dimension and epsilon-neighbourhood of discrete orbits generated by the unit-time map near nilpotent singularities are connected to the known bounds for local cyclicity of singularities. In this analysis, we use the restriction of the unit-time map on the characteristic curves or separatrices, depending on the type of singularity. Main nilpotent singularities which are studied here are nilpotent node, focus and cusp.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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