Pregled bibliografske jedinice broj: 1128780
Fractal analysis of planar nilpotent singularities and numerical applications
Fractal analysis of planar nilpotent singularities and numerical applications // Journal of differential equations, 293 (2021), 1-22 doi:10.1016/j.jde.2021.05.015 (međunarodna recenzija, članak, znanstveni)
CROSBI ID: 1128780 Za ispravke kontaktirajte CROSBI podršku putem web obrasca
Naslov
Fractal analysis of planar nilpotent singularities
and numerical applications
Autori
Horvat Dmitrović, Lana ; Huzak, Renato ; Vlah, Domagoj ; Županović, Vesna
Izvornik
Journal of differential equations (0022-0396) 293
(2021);
1-22
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Nilpotent singularity ; Box dimension ; Unit-time map ; Poincaré map ; Characteristic curve ; Numerical methods
Sažetak
The goal of our work is to give a complete fractal classification of planar analytic nilpotent singularities. For the classification, we use the notion of box dimension of (two-dimensional) orbits on separatrices generated by the unit time map. We also show how the box dimension of the one- dimensional orbit generated by the Poincaré map defined on the characteristic curve near the nilpotent center/focus, reveals an upper bound for the number of limit cycles near the singularity. We introduce simple formulas for numerical calculation of the box dimension of one- and two-dimensional orbits and apply them to nilpotent singularities.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Ustanove:
Fakultet elektrotehnike i računarstva, Zagreb
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
