We consider perturbations of integrable, area preserving non-twist maps of the annulus (those are maps that violate the twist condition in a very strong sense: @q 0 =@p changes sign). These maps appear in a variety of applications, notably transport in atmospheric Rossby waves. We show in suitable 2-parameter families the persistence of critical circles (invariant circles whose rotation number ...

We consider perturbations of integrable, area preserving non-twist maps of the annulus (those are maps in which the twist condition changes sign). These maps appear in a variety of applications, notably transport in atmospheric Rossby waves. We show in suitable 2-parameter families the persistence of critical circles (invariant circles whose rotation number is the maximum of all the rotation nu...

We consider perturbations of integrable area preserving non twist maps of the annulus those are maps in which the twist condition changes sign These maps appear in a variety of applications notably transport in atmospheric Rossby waves We show in suitable parameter families the persistence of critical circles invariant circles whose rotation number is the maximum of all the rotation numbers of ...

We show that if a Lie group acts properly on a co-oriented contact manifold preserving the contact structure then the contact quotient is topologically a stratified space (in the sense that a neighborhood of a point in the quotient is a product of a disk with a cone on a stratified space). As a corollary we obtain that symplectic quotients for proper Hamiltonian actions are topologically strati...

The existing constructions of derived Lie and sh-Lie brackets involve multilinear maps that are used to define higher order differential operators. In this paper, we prove the equivalence of three different definitions of higher order operators. We then introduce a unifying theme for building derived brackets and show that two prevalent derived Lie bracket constructions are equivalent. Two basi...

We show that any finite system S in a characteristic zero integral domain can be mapped to Z/pZ, for infinitely many primes p, preserving all algebraic incidences in S. This can be seen as a generalization of the well-known Freiman isomorphism lemma, which asserts that any finite subset of a torsion-free group can be mapped into Z/pZ, preserving all linear incidences. As applications, we derive...

We prove some results about solvable Lie algebras endowed with a reductive action of a fixed Lie algebra. The first application consists in proving that if g is a Lie algebra over a local field of characteristic zero whose “amenable radical” is not a direct factor, then g contains a subalgebra which is isomorphic to the semidirect product of sl2 by either a nontrivial irreducible representation...

1 Ergodic theory References for this section: CFS]. 1. The basic setting of ergodic theory: a measure-preserving transformation T of a probability space (X; B; m). Usually we assume T is invertible. (More generally, measure-preserving means R f T = R f; equivalently, m(T ?1 (A)) = mA.) How many measure spaces are there? Standard Borel spaces: any Borel subset of a complete, separable metric spa...