A note on pseudo resolvents

A note on pseudo - symplectic Runge - Kutta

In 1], the concept of pseudo-symplecticness was introduced in order to construct explicit Runge-Kutta methods which mimic symplectic ones. Of particular interest are methods of order (p; 2p),-i.e. of order p and pseudo-symplecticness order 2p-, for which the growth of the global error remains linear. The aim of this note is to show the existence of methods of orders (4; 8) and (5; 10) with a mi...

Spectral properties of pseudo-resolvents under structured perturbations

On smooth local resolvents

We exhibit an example of a bounded linear operator on a Banach space which admits an everywhere defined local resolvent with continuous derivatives of all orders. Let T be a bounded linear operator acting on a complex Banach space X. It is well known that the resolvent z 7→ (T − z)−1 defined on the complement of the spectrum σ(T ) is unbounded. More precisely, ‖(T − z)−1‖ → ∞ whenever z approac...

A Note on an Unusual Characterization of the Pseudo-arc

Lewis showed that the pseudo-arc is the unique nondegenerate continuum having the property that any two copies of it that are setwise near each other in terms of the Hausdorff distance are homeomorphically near each other. We present a new proof of this fact based on a well-known result of Bing, standard facts from infinite-dimensional topology and the Effros Theorem.

A Note on Pseudo-Anosov Maps with Small Growth Rate

We present an explicit sequence of pseudo-Anosov maps φk : S2k → S2k of surfaces of genus 2k whose growth rates converge to one. Introduction In this note, we present an explicit sequence φk of pseudo-Anosov of surfaces of genus 2k whose growth rates converge to one. This answers a question of Joan Birman, who had previously asked whether such growth rates are bounded away from one. Norbert A’C...