Naslov
Box dimension as specific property of hyperbolic and nonhyperbolic fixed points and singularities of dynamical systems in R^n

Autori
Horvat Dmitrović, Lana

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

Izvornik
6th Croatian Mathematical Congress / - Zagreb, 2016

Skup
6th Croatian Mathematical Congress

Mjesto i datum
Zagreb, Hrvatska, 14.06.2016. - 17.06.2016

Vrsta sudjelovanja
Poster

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
box dimension, hyperbolic/nonhyperbolic, fixed point, singularity, center manifold

Sažetak
This article is a study of box dimensions of hiperbolic and nonhyperbolic fixed points or singularities. We study the box dimension of an orbit around the hyperbolic and nonhyperbolic fixed point in the discrete dynamical systems. It is already known that the orbits around the hyperbolic fixed point in one-dimensional discrete dynamical system has the box dimension equal to zero. In this paper we generalise that result to n dimensions, that is, we show that the box dimension of an orbit equals 0 is property of hyperbolic fixed points of discrete dynamical systems in higher dimensions. On the other hand, near nonhyperbolic fixed points orbits have positive box dimension. In the process of determining values of box dimension we use the stable, unstable and center manifolds of systems. We also apply this results to the hyperbolic and nonhyperbolic singularities of continuous dynamical systems by using the unit-time map.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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