The exponential map is chaotic: An invitation to transcendental dynamics

We present an elementary and conceptual proof that the complex exponential map is "chaotic" when considered as a dynamical system on the complex plane. (This result was conjectured by Fatou in 1926 and first proved by Misiurewicz 55 years later.) The only background required is a first undergraduate course in complex analysis.Comment: 22 pages, 4 figures. (Provisionally) accepted for publication the American Mathematical Monthly. V2: Final pre-publication version. The article has been revised, corrected and shortened by 14 pages; see Version 1 for a more detailed discussion of further properties of the exponential map and wider transcendental dynamic

Indexing, screening, coding and cataloging of earth resources aircraft mission data

Tasks completed are as follows: (1) preparation of large Area Crop Inventory experiment for data base entry;(2) preparation of Earth Observations Aircraft Flight summary reports for publication; (3) updating of the aircraft mission index coverage map and Ames aircraft flight map; (4) Prepared of Earth Observation Helicopter Flight reports for publication; and (5) indexing of LANDSAT imagery. (6) formulation of phase 3 biowindows 1, 2, 3, and 4 listings by country, footprint, and acqusition dates; (7) preparation of flight summary reports; and (8) preparation of an Alaska state index coverage map

Fixed Point Indices and Manifolds with Collars

This paper concerns a formula which relates the Lefschetz number L(f) for a map f:M --> M' to the fixed point index I(f) summed with the fixed point index of a derived map on part of the boundary of M. Here M is a compact manifold and M' is M with a collar attached.Comment: Accepted for publication in Fixed Point Theory and Applications as part of the proceedings of the Newfoundland conference on fixed points, 200

Vanishing quantum discord is necessary and sufficient for completely positive maps

Two long standing open problems in quantum theory are to characterize the class of initial system-bath states for which quantum dynamics is equivalent to (1) a map between the initial and final system states, and (2) a completely positive (CP) map. The CP map problem is especially important, due to the widespread use of such maps in quantum information processing and open quantum systems theory. Here we settle both these questions by showing that the answer to the first is "all", with the resulting map being Hermitian, and that the answer to the second is that CP maps arise exclusively from the class of separable states with vanishing quantum discord.Comment: 4 pages, no figures. v2: Accepted for publication in Phys. Rev. Let

Mapping of quantum well eigenstates with semimagnetic probes

We present results of transmission measurements on CdTe quantum wells with thin semimagnetic CdMnTe probe layers embedded in various positions along the growth axis. The presence of the probes allow us to map the probability density functions by two independent methods: analyzing the exciton energy position and the exciton Zeeman splitting. We apply both approaches to map the first three quantum well eigenstates and we find that both of them yield equally accurate results.Comment: Accepted for publication in Physical Review