Naslov
Normal forms for strongly hyperbolic logarithmic transseries and Dulac germs

Autori
Peran, Dino

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

Skup
Bifurcation of Dynamical Systems and Numerics

Mjesto i datum
Zagreb, Hrvatska, 09.05.2023. - 11.05.2023

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Podatak o recenziji nije dostupan

Ključne riječi
fixed point theory, strongly hyperbolic fixed point, Dulac germs, logarithmic transseries, normal forms, normalizations

Sažetak
In this talk we obtain formal normal forms for strongly hyperbolic logarithmic transseries f=x^a+…, a>1, using fixed point theorems. We show that we can obtain formal normalization algorithmically by iterating suitable logarithmic transseries taken as an initial condition. Using this result we obtain formal normalizations of strongly hyperbolic Dulac germs. Therefore, we first present result about analytic normalizations of analytic germs on suitable complex domains, having strongly hyperbolic asymptotic bounds, and then we combine these formal and analytic results to prove that normalization of a strongly hyperbolic Dulac germ has the analytic formal normalization as its asymptotic expansion. Thus, the analytic normalization of a strongly hyperbolic Dulac germ is again a Dulac germ. This result can be viewed as an analogue of the classical Böttcher theorem.

Izvorni jezik
Engleski

POVEZANOST RADA