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Advances on Stable Ergodicity of Toral Automorphisms
Fernando Argentieri, Andrea Ulliana
We prove that all ergodic automorphisms of the -dimensional torus with two dimensional center are stably ergodic. This includes all ergodic automorphisms in dimension …
Ergodicity of skew-products over typical IETs
Fernando Argentieri, Przemysław Berk, Frank Trujillo
We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form \[ {T_f}:{[0, 1) \times \mathbb{R}}\to{…
On the linearization of analytic diffeomorphisms of the torus
Fernando Argentieri, Livia Corsi
We provide an arithmetic condition weaker then the Bryuno condition for which it is possible to apply a KAM scheme in dimension greater then one. The KAM scheme will be provided in…
Isolated Diophantine numbers
Fernando Argentieri, Luigi Chierchia
In this short note, we discuss the topology of Diophantine numbers, giving simple explicit examples of Diophantine isolated numbers (among those with same Diophantine constatnts),…
Diophantine sets in general are Cantor sets
Fernando Argentieri
Let and define the " Diophantine set" as: $$D_{γ,τ}:=\{α\in (0;1): ||qα||\geq\fracγ{q^τ}\quad\forall q\in\Bbb{N}\},\qquad||x||:=\inf_{p\in\Bbb{Z}…