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We completely describe the weak closure of the powers of the Koopman operator associated to Chacons classical automorphism. We show that weak limits of these powers are the ortho-projector to constants and an explicit family of polynomials. As a consequence, we answer negatively the question of alpha-weak mixing for Chacons automorphism.
In this article we study automorphisms of Toeplitz subshifts. Such groups are abelian and any finitely generated torsion subgroup is finite and cyclic. When the complexity is non superlinear, we prove that the automorphism group is, modulo a finite c
We study the geometry and dynamics of discrete subgroups $Gamma$ of $PSL(3,mathbb{C})$ with an open invariant set $Omega subset PC^2$ where the action is properly discontinuous and the quotient $Omega/Gamma$ contains a connected component whicis comp
It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $mathbb{Z}$ [DDPM15, CK15]. In this article we extend this result to a broader class proving that the automorphism group o
Let $f$ be an endomorphism of the projective line. There is a natural conjugation action on the space of such morphisms by elements of the projective linear group. The group of automorphisms, or stabilizer group, of a given $f$ for this action is kno
Given an ideal $I=(f_1,ldots,f_r)$ in $mathbb C[x_1,ldots,x_n]$ generated by forms of degree $d$, and an integer $k>1$, how large can the ideal $I^k$ be, i.e., how small can the Hilbert function of $mathbb C[x_1,ldots,x_n]/I^k$ be? If $rle n$ the sma