Naslov
Epsilon-neighbourhoods of orbits and formal classification of parabolic diffeomorphisms

Autori
Resman, Maja

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

Izvornik
Book of Abstracts 5th CroMC / Crnković, Dean ; Mikulić Crnković, Vedrana ; Rukavina, Sanja - Rijeka, 2012

ISBN
978-953-7720-13-1

Skup
5th Croatian Mathematical Congress

Mjesto i datum
Rijeka, Hrvatska, 18.06.2012. - 21.06.2012

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
complex parabolic diffeomorphisms; box dimension; Minkowski content; formal normal form

Sažetak
The talk is about local discrete dynamics generated by parabolic diffeomorphisms f : C -> C tangent to the identity with fixed point at the origin. Precisely, we show how formal classification of a given parabolic diffeomorphism can be deduced from two coefficients in formal asymptotic development of the epsilon−neighbourhood of one of its orbits near the origin, without making the usual change of variables which lead to formal normal form. On the other hand, relevant coefficients and constants are not without the geometric meaning: they present fractal properties of the orbit, namely its box dimension, Minkowski content and so called residual content. The results can be applied to formal classification of complex saddles using their holonomy maps, which, under some assumptions on the saddle, turn out to be parabolic diffeomorphisms.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA