1995 The dissertation of Slobodan Simi c is approved, and is acceptable in quality and form for publication on microolm: Chair Date Date Date 1 Abstract Anosov Flows of Codimension One The main goal of this dissertation is to show the existence of global cross sections for certain classes of Anosov ows. Let be a C 2 codimension one Anosov ow on a compact Riemannian manifold M of dimension great...

This article investigates the codimension of commutator spaces [I, B(H)] of operator ideals on a separable Hilbert space, i.e., “How many traces can an ideal support?” We conjecture that the codimension can be only zero, one, or infinity. Using the arithmetic mean (am) operations on ideals introduced in [13] and the analogous arithmetic mean operations at infinity (am-∞) that we develop extensi...

We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of characteristic zero. We compute this invariant for all complex nilpotent Lie algebras of dimension n ≤ 7. Furthermore we study the case where there exists an...

We show that every codimension one partially hyperbolic diffeomorphism must support on ${ \mathbb{T}}^{n} $. It is locally uniquely integrable and derived from a linear Anosov diffeomorphism. Moreover, this system intrinsically ergodic, the A. Katok's conjecture about existence of ergodic measures with intermediate entropies holds for it.

Abstract Following Losik’s approach to Gelfand’s formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions nontriviality in terms of dynamical properties generators holonomy groups found. The Reeb is shown; this contrast with some classical theorems on Godbillon-Vey class; example, Mizutani-Morit...