Let f : X → X be a map of a compact, connected Riemannian manifold, with or without boundary. For > 0 sufficiently small, we introduce an -Nielsen number N ( f ) that is a lower bound for the number of fixed points of all self-maps of X that are -homotopic to f . We prove that there is always a map g : X → X that is -homotopic to f such that g has exactlyN ( f ) fixed points. We describe proced...

There is evidence that the conventional, continuous underlying function model of financial asset pricing can be improved by adding a discontinuous jump component. Barndorff-Nielsen and Shephard (2004) propose a method of detecting these jumps that compares different estimators of quadratic variation. This paper applies that detection method to the common stock of Altria Group, Inc. and attempts...

To try to outperform an externally given benchmark with known weights is the most common equity mandate in the financial industry. For quantitative investors, this task is predominantly approached by optimizing their portfolios consecutively over short time horizons with one-period models. We seek in this paper to provide a theoretical justification to this practice when the underlying market i...

A well-known lower bound for the number of xed points of a self-map f : X ?! X is the Nielsen number N(f). Unfortunately, the Nielsen number is diicult to calculate. The Lefschetz number L(f), on the other hand, is readily computable, but does not give a lower bound for the number of xed points. In this paper, we investigate conditions on the space X which guarantee either N(f) = jL(f)j or N(f)...

In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. Here we extend it to pairs (f1, f2) of maps between manifolds of arbitrary dimensions. This leads to estimates of the minimum numbers MCC(f1, f2) (and MC(f1, f2), resp.) of pathcomponents (and of points, resp.) in the coincidence sets of those pairs of maps which are homotopic to (...

Overview: The Nielsen-Thurston Classification Theorem asserts that every element of MCG(Sg) (g ≥ 2) exhibits one of three types of simple behavior. It either has finite order, fixes a nonempty set of of isotopy classes of essential, simple closed curves (reducible), or stretches along a pair of transverse measured foliations in an area-preserving way (pseduo-Anosov). Bers’ strategy for proving ...

In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations), two main approaches are presented. The first is via Poincaré’s translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links wit...

Investigators since Freud have appreciated that memories of the people, places, activities and emotions of daily life are reflected in dreams but are typically so fragmented that their predictability is nil. The mechanisms that translate such memories into dream images remain largely unknown. New research targeting relationships between dreaming, memory and the hippocampus is producing a new th...