Related papers: Real-analytic AbC constructions on the torus

We completely characterize real Bott manifolds up to affine diffeomorphism in terms of three simple matrix operations on square binary matrices obtained from strictly upper triangular matrices by permuting rows and columns simultaneously.…

The main result of this paper is that two large collections of ergodic measure preserving systems, the Odometer Based and the Circular Systems have the same global structure with respect to joinings. The classes are canonically isomorphic…

We develop a thermodynamic formalism for a class of diffeomorphisms of a torus that are "almost-Anosov". In particular, we use a Young tower construction to prove the existence and uniqueness of equilibrium states for a collection of…

Affine matrix-ball construction (abbreviated AMBC) was developed by Chmutov, Lewis, Pylyavskyy, and Yudovina as an affine generalization of Robinson-Schensted correspondence. We show that AMBC gives a simple way to compute a distinguished…

We consider two C^2 Anosov diffeomorphisms in a C^1 neighborhood of a linear hyperbolic automorphism of three dimensional torus with real spectrum. We prove that they are C^1+ conjugate if and only if the differentials of the return maps at…

This paper is part 1 of a series of papers culminating in the result that measure preserving diffeomorphisms of the disc or 2-torus are unclassifiable. It also addresses another classical problem: which abstract measure preserving systems…

In this article we utilise abstract convexity theory in order to unify and generalize many different concepts from nonsmooth analysis. We introduce the concepts of abstract codifferentiability, abstract quasidifferentiability and abstract…

This paper deals with the problem of conjugacy of Cartan subalgebras for affine Kac-Moody Lie algebras. Unlike the methods used by Peterson and Kac, our approach is entirely cohomological and geometric. It is deeply rooted on the theory of…

We construct area-preserving real analytic diffeomorphisms of the torus with unbounded growth sequences of arbitrarily slow growth.

We show how one can do algebraic geometry with respect to the category of simplicial objects in an exact category. As a biproduct, we get a theory of derived analytic geometry.

In [23], Slipantschuk, Bandtlow and Just gave concrete examples of Anosov diffeomorphisms of the two-torus for which their resonances could be completely described. Their approach was based on composition operators acting on analytic…

If a non-ergodic, partially hyperbolic diffeomorphism on the 3-torus is homotopic to an Anosov diffeomorphism $A$, it is topologically conjugate to $A$.

We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points and which are not conjugated to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen…

We examine a unique construction of the real numbers which proceeds directly from the integers using approximately linear-endomorphisms with finite error, called near-endomorphisms. In this paper, we show that the set of near-endomorphisms…

The continuity, in a suitable topology, of algebraic and geometric operations on real analytic manifolds and vector bundles is proved. This is carried out using recently arrived at seminorms for the real analytic topology. A new…

In this paper, we develop a toric analog of the theory of adelic divisors on quasi-projective arithmetic varieties introduced by Yuan and Zhang, and extend the convex-analytic descriptions of the Arakelov geometry of projective toric…

In this paper we further the study of arrow algebras, simple algebraic structures inducing toposes through the tripos-to-topos construction, by defining appropriate notions of morphisms between them which correspond to morphisms of the…

This paper shows any non-Anosov partially hyperbolic diffeomorphism on the 3-torus which is homotopic to Anosov must be accessible.

We investigate a phenomenon observed by W. Thurston wherein one constructs a pseudo-Anosov homeomorphism on the limit set of a certain lift of a piecewise-linear expanding interval map. We reconcile this construction with a special subclass…

In this paper we construct abelian extensions of the group of diffeomorphisms of a torus. We consider the jacobian map, which is a crossed homomorphism from the group of diffeomorphisms into a toroidal gauge group. A pull-back under this…