We study partially hyperbolic diffeomorphisms satisfying a trapping property which makes them look as if they were Anosov at large scale. We show that, as expected, they share several properties with Anosov diffeomorphisms. We construct an expansive quotient of the dynamics and study some dynamical consequences related to this quotient.

Let S be a closed surface of genus g ≥ 2. A finitely generated group Γ S is an extension of the fundamental group π 1 (S) of S if π 1 (S) is a normal subgroup of Γ S. We show that the group Γ S is hyperbolic if and only if the orbit map for the action of the quotient group Γ = Γ S /π 1 (S) on the complex of curves is a quasi-isometric embedding.

This document discusses a numerical analysis method for low thrust trajectory propagation known as the proximity quotient or Q-Law. The process uses a Lyapunov feedback control law developed by Petropoulos [1] to propagate trajectories of spacecraft by minimizing the user defined function at the target orbit. A simplified propagator is created from the core mechanics of this method in MATLAB an...

1 13 4. Free rational curves 14 5. Uniruledness 16 5.1. Definitions equivalent to uniruledness 16 5.2. Examples and consequences of uniruledness 18 6. Rational connectivity 20 6.1. Definitions equivalent to rational connectivity 21 6.2. Rational chain-connectivity implies rational connectivity 22 6.3. Examples and consequences of rational connectivity 26 7. The MRC quotient 27 7.1. Quotients by...

This paper focuses on the relationships between bilingualism, intelligence quotient (IQ) and errors made by learners in their attempt to master the rules of the target language(s). The first part of the paper explains the true nature of bilingualism contrarily to the controversial and stereotyped definitions found in the previous literature of the 1950’s: the author refers to Weinreich’s and Su...

The algorithms for linear algebra in the Magma and Axiom computer algebra systems work over an arbitrary ring. For example, the implementation of Gaussian elimination for reducing a matrix to (reduced) row Echelon form works over any field that the user constructs. In contrast, Maple’s facilities for linear algebra in its LinearAlgebra package only work for specific rings. If the input matrix c...

The symmetric group S3 acts on S 2 × S 2 × S 2 by coordinate permutation, and the quotient space (S 2×S 2×S )/S3 is homeomorphic to the complex projective space CP 3. In this paper, we construct an 124-vertex simplicial subdivision (S 2 ×S 2 ×S )124 of the 64vertex standard cellulation S 2 4 × S 2 4 × S 2 4 of S 2 × S 2 × S 2, such that the S3-action on this cellulation naturally extends to an ...

We describe hypergeometric functions of Deligne-Mostow type for open subsets of the configuration space of six points on P, induced from those for seven points on P. The seven point ball quotient example DM(2, 1) does not appear on Mostow’s original list [9], but does appear on Thurston’s corrected version [12]. We show that DM(2, 1) is a finite cover of the moduli space of cubic surfaces MC en...

We study the notion of a strongly normal sequence in the dual E∗ of a Banach space E. In particular, we prove that the following three conditions are equivalent: (1) E∗ has a strongly normal sequence, (2) (E∗, σ(E∗, E)) has a Schauder basic sequence, (3) E has an infinite-dimensional separable quotient.