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Finitarily Bernoulli factors are dense

Stephen Shea (2013)

Fundamenta Mathematicae

It is not known if every finitary factor of a Bernoulli scheme is finitarily isomorphic to a Bernoulli scheme (is finitarily Bernoulli). In this paper, for any Bernoulli scheme X, we define a metric on the finitary factor maps from X. We show that for any finitary map f: X → Y, there exists a sequence of finitary maps fₙ: X → Y(n) that converges to f, where each Y(n) is finitarily Bernoulli. Thus, the maps to finitarily Bernoulli factors are dense. Let (X(n)) be a sequence of Bernoulli schemes such...

Finitary orbit equivalence and measured Bratteli diagrams

T. Hamachi, M. S. Keane, M. K. Roychowdhury (2008)

Colloquium Mathematicae

We prove a strengthened version of Dye's theorem on orbit equivalence, showing that if the transformation structures are represented as finite coordinate change equivalence relations of ergodic measured Bratteli diagrams, then there is a finitary orbit equivalence between these diagrams.

Finite determinacy of dicritical singularities in ( ℂ 2 , 0 )

Gabriel Calsamiglia-Mendlewicz (2007)

Annales de l’institut Fourier

For germs of singularities of holomorphic foliations in ( ℂ 2 , 0 ) which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.

Finite-dimensional Pullback Attractors for Non-autonomous Newton-Boussinesq Equations in Some Two-dimensional Unbounded Domains

Cung The Anh, Dang Thanh Son (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

We study the existence and long-time behavior of weak solutions to Newton-Boussinesq equations in two-dimensional domains satisfying the Poincaré inequality. We prove the existence of a unique minimal finite-dimensional pullback D σ -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms.

Finite-dimensionality of 2-D micropolar fluid flow with periodic boundary conditions

Piotr Szopa (2007)

Applicationes Mathematicae

This paper is devoted to proving the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate their number. We check how the distribution of the forces and moments through modes influences the estimate of the number of determining modes. We also estimate the dimension of the global attractor. Finally, we compare our results with analogous results for the Navier-Stokes equation.

Finiteness of Ergodic Unitarily Invariant Measures on Spaces of Infinite Matrices

Alexander I. Bufetov (2014)

Annales de l’institut Fourier

The main result of this note, Theorem 1.3, is the following: a Borel measure on the space of infinite Hermitian matrices, that is invariant and ergodic under the action of the infinite unitary group and that admits well-defined projections onto the quotient space of “corners" of finite size, must be finite. A similar result, Theorem 1.1, is also established for unitarily invariant measures on the space of all infinite complex matrices. These results imply that the infinite Hua-Pickrell measures...

First steps in stable Hamiltonian topology

Kai Cieliebak, Evgeny Volkov (2015)

Journal of the European Mathematical Society

In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; stable Hamiltonian structures are generically Morse-Bott (i.e. all closed orbits are Bott nondegenerate) but not Morse; the standard contact structure on S 3 is homotopic to a stable Hamiltonian structure which cannot be embedded in ℝ 4 . Moreover, we derive a structure theorem for stable...

Fixed points of discrete nilpotent group actions on S 2

Suely Druck, Fuquan Fang, Sebastião Firmo (2002)

Annales de l’institut Fourier

We prove that for each integer k ≥ 2 there is an open neighborhood 𝒱 k of the identity map of the 2-sphere S 2 , in C 1 topology such that: if G is a nilpotent subgroup of Diff 1 ( S 2 ) with length k of nilpotency, generated by elements in 𝒱 k , then the natural G -action on S 2 has nonempty fixed point set. Moreover, the G -action has at least two fixed points if the action has a finite nontrivial orbit.

Flat 3-webs of degree one on the projective plane

A. Beltrán, M. Falla Luza, D. Marín (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The aim of this work is to study global 3 -webs with vanishing curvature. We wish to investigate degree 3 foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree 3 foliations whose Legendre transform are webs with zero curvature.

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