Naslov
Multiplicity of fixed points and growth of varepsilon-neighbourhoods of orbits

Autori
Vesna Županović, Pavao Mardešić, Maja Resman

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

Izvornik
Fifth Croatian Mathematical Congress / - Rijeka : Sveučilište u Rijeci, HMD, 2012

Skup
Fifth Croatian Mathematical Congress

Mjesto i datum
Rijeka, Hrvatska, 18.06.2012. - 21.06.2012

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Domaća recenzija

Ključne riječi
Multiplicity; Cyclicity; Chebyshev system

Sažetak
We study the relationship between the multiplicity of a fixed point of a function g, and the dependence on ε of the length of ε-neighborhood of any orbit of g, tending to the fixed point. The relationship between these two notions was discovered in [5] for the differentiable case, and related to the box dimension of the orbit. Here, we generalize these results to non- differentiable cases introducing a new notion of critical Minkowski order. We study the space of functions having a development in a Chebyshev scale and use multiplicity with respect to this space of functions. With the new definition, we recover the relationship between multiplicity of fixed points and the dependence on ε of the length of ε- neighborhoods of orbits in non-differentiable cases. Applications include in particular Poincaré maps near homoclinic loops and hyperbolic 2- cycles, and Abelian integrals. This is a new approach to estimate the cyclicity, by computing the length of the ε-neighborhood of one orbit of the Poincaré map (for example numerically), and by comparing it to the appropriate scale.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA