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Pregled bibliografske jedinice broj: 1012168

Towards bifurcations of complex dimensions


Lapidus, Michel L.; Radunović, Goran; Žubrinić, Darko
Towards bifurcations of complex dimensions // Equadiff 2019: Book of Abstracts
Leiden, Nizozemska, 2019. str. 89-89 (predavanje, međunarodna recenzija, sažetak, znanstveni)


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Naslov
Towards bifurcations of complex dimensions

Autori
Lapidus, Michel L. ; Radunović, Goran ; Žubrinić, Darko

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

Izvornik
Equadiff 2019: Book of Abstracts / - , 2019, 89-89

Skup
Equadiff 2019

Mjesto i datum
Leiden, Nizozemska, 08-12.07.2019

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
bifurcations ; complex dimensions, fractal zeta function, fracctal set, Minkowski content

Sažetak
It is known that at the moment when a limit cycle is born from a weak focus in a Hopf-Takens bifurcation, the Minkowski dimension of any associated spiral trajectory jumps from trivial, i.e., 1 to nontrivial, i.e. a rational number of the form 4k/(2k+1) where the integer k is the multiplicity of the weak focus. For a given set, its complex dimensions are defined as the poles of the associated fractal distance zeta function and provide a far-reaching generalization of the classical notion of the Minkowski dimension. The higher-dimensional theory of complex dimensions has been developed in the recent extensive research monograph by the co-authors. One defines the order of a given complex dimension as the order of the pole of the associated fractal zeta function. We show on a geometric example of a fractal nest the effect of merging of two simple complex dimensions of order one into a single complex dimension of order 2. This is interesting since the fractal nest can be considered as a geometric simplification of a focus trajectory of a dynamical system. We conjecture that this effect of merging of several complex dimensions into a single one can give new insights into bifurcations of dynamical systems.

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
HRZZ-UIP-2017-05-1020 - Fraktalna analiza diskretnih dinamičkih sustava (DSfracta) (Resman, Maja, HRZZ - 2017-05 )

Ustanove
Fakultet elektrotehnike i računarstva, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb

Profili:

Avatar Url Darko Žubrinić (autor)

Avatar Url Goran Radunović (autor)

Citiraj ovu publikaciju

Lapidus, Michel L.; Radunović, Goran; Žubrinić, Darko
Towards bifurcations of complex dimensions // Equadiff 2019: Book of Abstracts
Leiden, Nizozemska, 2019. str. 89-89 (predavanje, međunarodna recenzija, sažetak, znanstveni)
Lapidus, M., Radunović, G. & Žubrinić, D. (2019) Towards bifurcations of complex dimensions. U: Equadiff 2019: Book of Abstracts.
@article{article, year = {2019}, pages = {89-89}, keywords = {bifurcations, complex dimensions, fractal zeta function, fracctal set, Minkowski content}, title = {Towards bifurcations of complex dimensions}, keyword = {bifurcations, complex dimensions, fractal zeta function, fracctal set, Minkowski content}, publisherplace = {Leiden, Nizozemska} }




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