Related papers: Orbit equivalence for Cantor minimal Z^2-systems

Over an algebraically closed field, we described a minimal set of representatives for G_2-orbits on the set of pairs of octonions.

We construct Ahlfors regular Cantor sets $K$ of small dimension in the plane, such that the Hausdorff measure on $K$ is equivalent to the harmonic measure associated to its complement. In particular the Green function in $R^2 \backslash K$…

Transport in near-integrable, but partially chaotic, $1 1/2$ degree-of-freedom Hamiltonian systems is blocked by invariant tori and is reduced at \emph{almost}-invariant tori, both associated with the invariant tori of a neighboring…

In a finite real reflection group, two factorizations of a Coxeter element into an arbitrary number of reflections are shown to lie in the same orbit under the Hurwitz action if and only if they use the same multiset of conjugacy classes.…

We give an elementary proof for Lewis Bowen's theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our methods also show that for all compact groups K and…

We study asymptotic continuous orbit equivalence of Smale spaces. We prove that two irreducible Smale spaces are flip conjugate if and only if there exists a periodic point preserving homeomorphism giving an asymptotic continuous orbit…

A minimal Cantor system is said to be self-induced whenever it is conjugate to one of its induced systems. Substitution subshifts and some odometers are classical examples, and we show that these are the only examples in the equicontinuous…

This paper is about the existence of periodic orbits near an equilibrium point of a two-degree-of-freedom Hamiltonian system. The equilibrium is supposed to be a nondegenerate minimum of the Hamiltonian. Every sphere-like component of the…

In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minimal systems is…

We prove Yun's minimal reduction conjecture for all classical groups. More precisely, for any topologically nilpotent regular semisimple element $\gamma$, we show that the associated minimal reduction set…

In the first part of the paper, we introduce notions of asymptotic continuous orbit equivalence and asymptotic conjugacy in Smale spaces and characterize them in terms of their asymptotic Ruelle algebras with their dual actions. In the…

We introduce higher order regionally proximal relations suitable for an arbitrary acting group. For minimal abelian group actions, these relations coincide with the ones introduced by Host, Kra and Maass. Our main result is that these…

We define a real $A$ to be low for paths in Baire space (or Cantor space) if every $\Pi^0_1$ class with an $A$-computable element has a computable element. We prove that lowness for paths in Baire space and lowness for paths in Cantor space…

We survey the recent history of the conformal Calabi-Yau problem consisting in determining the complex structures admitted by complete bounded minimal surfaces in $\mathbb{R}^3$. Moreover, we prove that for any minimally convex domain…

We introduce dynamical systems $(X,G)$ with closed relations $G$ on compact metric spaces $X$ and discuss different types of minimality of such dynamical systems, all of them generalizing minimal dynamical systems $(X,f)$ with continuous…

We develop a two-orbital Hubbard model of electron correlations in ultrathin (111)-oriented fcc films of late transition metals such as Co and Ni. Our model indicates that the Mott-Hund's interaction results in ferromagnetic…

We show that given any subgroup F of R_+ which is either countable or belongs to a certain "large" class of uncountable subgroups, there exist continuously many free ergodic probability measure preserving actions \sigma_i of the free group…

We study some examples of minimal length curves in homogeneous spaces of B(H) under a left action of a unitary group. Recent results relate these curves with the existence of minimal (with respect to a quotient norm) anti-Hermitian…

We show that for every complex simple Lie algebra, the equations of Schubert divisors on the flag variety give a complete integrable system of the minimal nilpotent orbit. The approach is motivated by the integrable system on Coulomb…

We present a technique to map an electronic model with local interactions (a generalized multi-orbital Hubbard model) onto an effective model of interacting classical spins, by requiring that the thermodynamic potentials associated to spin…