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Arveson dichotomy and essential fractality
Arveson dichotomy essential spectral approximation essential fractality
2011/9/21
Abstract: The notions of fractal and essentially fractal algebras of approximation sequences and of the Arveson dichotomy have proved extremely useful for several spectral approximation problems. The ...
Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms
Essential hyperbolicity homoclinic bifurcations dichotomy phenomenon/mechanism for diffeomorphisms
2010/11/22
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional c...
Looking for a Billiard Table which is not a Lattice Polygon but Satisfies Veech's Dichotomy
Billiard Table Lattice Polygon Satisfies Veech's Dichotomy
2010/11/19
Over the course of studying billiard dynamics, several questions were raised. One of the questions was, which surfaces satisfy the following property (which is called Veech's dichotomy): Any directio...
Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation
the blowup/global existence dichotomy the focusing cubic nonlinear Klein-Gordon equation
2010/11/15
We present some numerical findings concerning the nature of the blowup vs. global existence dichotomy for the focusing cubic nonlinear Klein-Gordon equation in three dimensions for radial data. The co...
Dichotomy and periodic solutions of a kind of integro-differential equations
Periodic solution (h, k)-dichotomy integro-differential equations
2010/9/14
In the present paper, we investigate some important properties of (h, k)-dichotomy. rthermore, we study the higher dimensional periodic system
A dichotomy between uniform distributions of the Stern-Brocot and the Farey sequence
Uniform distribution (mod 1), Stern-Brocot sequence, Farey sequence,
2010/12/3
We employ infinite ergodic theory to show that the even Stern-Brocot sequence and the Farey sequence are uniformly distributed mod 1 with respect to certain canonical weightings. As a corollary we der...
The Filter Dichotomy says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamm...
Dichotomy theorems for random matrices and closed ideals of operators on $\big(\bigoplus_{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$
Dichotomy random matrices closed ideals of operators
2010/12/7
We prove two dichotomy theorems about sequences of operators into L1 given by random matrices. In the second theorem we assume that the entries of each random ma-trix form a sequence of independent, s...