Dilations associated to flat curves

Wavelets Associated with Composite Dilations

1 Basic definitions In this paper, we present a description of a collaboration with K. Guo, W. Lim, A. Savov and E. Wilson. We make use of the Fourier transform f → ˆ f that, for f ∈ L 1 (R n), is defined asˆf (ξ) = R n f (x) e −2πiξx dx. As is well-known, this operator has a unique extension to L 2 (R n) that is a unitary operator. In the following, we refer to the domain ofˆf as the " frequen...

Equidistribution of Dilations of Polynomial Curves in Nilmanifolds

In this paper we study the asymptotic behaviour under dilations of probability measures supported on smooth curves in nilmanifolds. We prove, under some mild conditions, effective equidistribution of such measures to the Haar measure. We also formulate a mean ergodic theorem for Rn-representations on Hilbert spaces, restricted to a moving phase of low dimension. Furthermore, we bound the necess...

Integrable Systems Associated to Curves in Flat Galilean and Lorentzian Manifolds

This article examines the relationship between geometric Poisson brackets and integrable systems in flat Galilean, and Lorentz manifolds. First, moving frames are used to calculate differential invariants of curves and to write invariant evolution equations. The moving frames are created to ensure that the Galilean moving frame is the limit of the Lorentz one as c → ∞. Then, associated integrab...

Limitations to maximum running speed on flat curves.

Why is maximal running speed reduced on curved paths? The leading explanation proposes that an increase in lateral ground reaction force necessitates a decrease in peak vertical ground reaction force, assuming that maximum leg extension force is the limiting factor. Yet, no studies have directly measured these forces or tested this critical assumption. We measured maximum sprint velocities and ...

Polyomorphisms Conjugate to Dilations