Alejandro Kocsard
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View article: Periodic point free homeomorphisms and irrational rotation factors
Periodic point free homeomorphisms and irrational rotation factors Open
We provide a complete characterization of periodic point free homeomorphisms of the $2$ -torus admitting irrational circle rotations as topological factors. Given a homeomorphism of the $2$ -torus without periodic points and exhibiting uni…
View article: The Burnside problem for Diffω(S2)
The Burnside problem for Diffω(S2) Open
A group $G$ is periodic of bounded exponent if there exists $k\\in \\mathbb{N}$ such that every element of $G$ has order at most $k$ . We show that every finitely generated periodic group of bounded exponent $G\\lt \\operatorname{Diff}_{\\…
View article: Kronecker factors for periodic point free homeomorphisms
Kronecker factors for periodic point free homeomorphisms Open
We provide a complete characterization of periodic point free homeomorphisms of the $2$-torus admitting irrational rotations as topological factors. Given a homeomorphism of the $2$-torus without periodic points and exhibiting uniformly bo…
View article: Livsic theorem for diffeomorphism cocycles
Livsic theorem for diffeomorphism cocycles Open
We prove the so called Livšic theorem for cocycles taking values in the group of $C^{1+β}-diffeomorphisms of any closed manifold of arbitrary dimension. Since no localization hypothesis is assumed, this result is completely global in the s…
View article: On the dynamics of minimal homeomorphisms of $\mathbb{T}^2$ which are not pseudo-rotations
On the dynamics of minimal homeomorphisms of $\mathbb{T}^2$ which are not pseudo-rotations Open
We prove that any minimal $2$-torus homeomorphism which is isotopic to the identity and whose rotation set is not just a point exhibits uniformly bounded rotational deviations on the perpendicular direction to the rotation set. As a conseq…
View article: Structural stability of the inverse limit of endomorphisms
Structural stability of the inverse limit of endomorphisms Open
We prove that every endomorphism which satisfies Axiom A and the strong transversality conditions is C^{1} -inverse limit structurally stable. These conditions were conjectured to be necessary and sufficient. This result is applied to the …
View article: The Burnside problem for $\text{Diff}_{\text{Vol}}(\mathbb{S}^2)$
The Burnside problem for $\text{Diff}_{\text{Vol}}(\mathbb{S}^2)$ Open
Let $S$ be a closed surface and $\text{Diff}_{\text{Vol}}(S)$ be the group of volume preserving diffeomorphisms of $S$. A finitely generated group $G$ is periodic of bounded exponent if there exists $k \in \mathbb{N}$ such that every eleme…
View article: Livšic theorem for low-dimensional diffeomorphism cocycles
Livšic theorem for low-dimensional diffeomorphism cocycles Open
We prove a Livšic type theorem for cocycles taking values in groups of diffeomorphisms of low-dimensional manifolds. The results hold without any localization assumption and in very low regularity. We also obtain a general result (in any d…
View article: On manifolds supporting distributionally uniquely ergodic diffeomorphisms
On manifolds supporting distributionally uniquely ergodic diffeomorphisms Open
A smooth diffeomorphism is said to be distributionally uniquely ergodic (DUE for short) when it is uniquely ergodic and its unique invariant probability measure is the only invariant distribution (up to multiplication by a constant). Ergod…