ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Дифференциальные Уравнения
и
Процессы Управления

Hedgehogs hunting with Cantor, Hausdorff and Liouville

Автор(ы):

Alessandro Rosa

Freelance programmer
c/o Locatelli,
Via Cappuccini 116/A,
I-72100 Brindisi, Italy

zandor_zz@yahoo.it

Аннотация:

We show the equivalence between Borel's regular sets model and the Liouville formula for the approximation of irrationals through rational numbers. The Diophantine-Liouville dichotomy can be resolved via sequences of transfinitely many approximants.

The existence of non-linearizable hedgehogs is purely theoretical and their electronic visualization is not feasible.

We show that the non-linearizable hedgehog for polynomials

is a locally connected, plane-filling Julia set with Hausdorff dimension 2, spreading radially everywhere inside a bounded non-empty region.

Полный текст (pdf)