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Box dimension as specific property of hyperbolic and nonhyperbolic fixed points and singularities of dynamical systems in R^n (CROSBI ID 647433)

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Horvat Dmitrović, Lana Box dimension as specific property of hyperbolic and nonhyperbolic fixed points and singularities of dynamical systems in R^n // 6th Croatian Mathematical Congress. Zagreb, 2016

Podaci o odgovornosti

Horvat Dmitrović, Lana

engleski

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

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.

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

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Podaci o prilogu

2016.

objavljeno

Podaci o matičnoj publikaciji

6th Croatian Mathematical Congress

Zagreb:

Podaci o skupu

6th Croatian mathematical congress

poster

14.06.2016-17.06.2016

Zagreb, Hrvatska

Povezanost rada

Matematika