相关论文: Two minimal unique ergodic diffeomorphisms on a ma…

For minimal unique ergodic diffeomorphisms $\alpha_n$ of $S^{2n+1} (n>0)$ and $\alpha_m$ of $S^{2m+1}(m>0)$, the $C^*$-crossed product algebra $C(S^{2n+1})\rtimes_{\alpha_n} \mathbb{Z}$ is isomorphic to $C(S^{2m+1})\rtimes_{\alpha_m}…

Let $X$ be an infinite compact metric space with finite covering dimension and let $\alpha, \beta : X\to X$ be two minimal homeomorphisms. We prove that the crossed product $C^*$-algebras $C(X)\rtimes_\alpha\Z$ and $C(X)\rtimes_\belta\Z$…

Let $(A, \alpha)$ and $(B, \beta)$ be C*-dynamical systems where $\alpha$ and $\beta$ are arbitrary *-endomorphisms. When $\alpha$ is injective or surjective, we show that the semicrossed products $A \times_\alpha \mathbb{Z}$ and $B…

Let $(\A, \alpha)$ and $(\B, \beta)$ be C*-dynamical systems and assume that $\A$ is a separable simple C*-algebra and that $\alpha$ and $\beta$ are *-automorphisms. Then the semicrossed products $\A \times_{\alpha} \bbZ^{+}$ and $\B…

We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal…

We prove that any $C^{1+\alpha}$ transitive conservative partially hyperbolic diffeomorphism of a closed 3-manifold with virtually solvable fundamental group is ergodic. Consequently, in light of \cite{FP-classify}, this establishes the…

We show that conservative partially hyperbolic diffeomorphism isotopic to the identity on Seifert 3-manifolds are ergodic.

Let $M$ be a smooth compact connected manifold of dimension $d\geq 2$, possibly with boundary, that admits a smooth effective $\mathbb{T}^2$-action $\mathcal{S}=\left\{S_{\alpha,\beta}\right\}_{(\alpha,\beta) \in \mathbb{T}^2}$ preserving a…

We consider diffeomorphisms in the $C^\infty$-closure of the conjugancy class of translations of the 2-torus. By a theorem of Fathi and Herman, a generic diffeomorphism in that space is minimal and uniquely ergodic. We define a new…

We prove the existence of a minimal diffeomorphism isotopic to the identity between two hyperbolic cone surfaces $(\Sigma,g_1)$ and $(\Sigma,g_2)$ when the cone angles of $g_1$ and $g_2$ are different and smaller than $\pi$. When the cone…

In this work we present an example of C^\infty-diffeomorphism of a compact 4-manifold such that it admits a global SRB measure \mu but for which the special ergodic theorem doesn't hold. Namely, for this transformation there exist a…

Let \beta : S^n \to S^n, for n = 2k + 1, k \geq 1, be one of the known examples of a non-uniquely ergodic minimal diffeomorphism of an odd dimensional sphere. For every such minimal dynamical system (S^n, \beta) there is a Cantor minimal…

We prove that for ergodic measures with large entropy have long unstable manifolds for $C^\infty$ surface diffeomorphisms. Specifically, for any $\alpha>0$, there exist constants $\beta>0$ and $c>0$ such that for every ergodic measure $\mu$…

In this paper we show that even in the case of simply connected minimal algebraic surfaces of general type, deformation and differentiable equivalence do not coincide. Exhibiting several simple families of surfaces which are not deformation…

Let $\beta: S^{2n+1}\to S^{2n+1}$ be a minimal homeomorphism ($n\ge 1$). We show that the crossed product $C(S^{2n+1})\rtimes_{\beta} \Z$ has rational tracial rank at most one. More generally, let $\Omega$ be a connected compact metric…

We prove that every $C^2$ conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergodicity Conjecture by Hertz-Hertz-Ures in the absence of…

It is proved that the semigroups $\mathrm{\mathbf{End}}(\boldsymbol{B}_{\omega})$ and $\mathrm{\mathbf{End}}(\boldsymbol{B}_{\mathbb{Z}})$ of the endomorphisms of the bicyclic semigroup $\boldsymbol{B}_{\omega}$ and the endomorphisms of the…

We prove that for every $\epsilon>0$ there exists a minimal diffeomorphism $f:\T^{2}\rightarrow\T^{2}$ of class $C^{3-\epsilon}$ and semiconjugate to an ergodic traslation, and have the following properties: zero entropy, sensitivity with…

We describe simplicity of the Stacey crossed product A\times_\beta \N in terms of conditions of the endomorphism \beta. Then, we use a characterization of the graph C*-algebras C*(E) as the Stacey crossed product…

Let $\mathcal{C}$ be a C*-algebra and $\alpha:\mathcal{C} \rightarrow \mathcal{C}$ a unital *-endomorphism. There is a natural way to construct operator algebras which are called semicrossed products, using a convolution induced by the…