Methods Using herbarium records from the Oklahoma Vascular Plants Database from 1903 to 2004, we reconstructed the spatial and temporal collection history of two alien invasive taxa (Lonicera japonica and Tamarix spp.) and three native expansive species (Ambrosia psilostachya, Amphiachyris dracunculoides and Juniperus virginiana). To compare the overall collecting trend, groups of native non-ex...

We consider the problem of straightening chains in d ≥ 3 dimensions, possibly embedded into higher dimensions, using expansive motions. For any d ≥ 3, we show that there is an open chain in d dimensions that is not straight and not self-touching yet has no expansive motion. Furthermore, for any ∆ > 0 and d ≥ 3, we show that there is an open chain in d dimensions that cannot be straightened usin...

A framework for understanding the geometry of continuous actions of Z was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z-actions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the ...

A framework for understanding the geometry of continuous actions of Z was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z-actions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the ...

We investigate the interrelationships between the dynamical properties of commuting continuous maps of a compact metric space. Let X be a compact metric space. First we show the following. If τ : X → X is an expansive onto continuous map with the pseudo-orbit tracing property (POTP) and if there is a topologically mixing continuous map φ : X → X with τφ = φτ , then τ is topologically mixing. If...

Computer-Aided Manufacturing (CAM) occupies an increasingly important role in engineering with all it has to offer in terms of new possibilities and improving designer/manufacturer productivity. The present study addresses machining of free-form surfaces on a 3-axis NCmachine tool. There have recently been a large number of studies devoted to planning tool paths on free-form surfaceswith variou...

We show that topologically expansive Lorenz maps can be described up to topological conjugacy by their kneading invariants. We also give a simple condition on pairs of symbol sequences which is satisfied if and only if that pair of sequences is the kneading invariant for some topologically expansive Lorenz map. A simple extension of the theorems to the case of expansive maps of the interval wit...