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AbstractLet (X, d) be a metric space and fbe a continuous map from Xto X. Denote by ω(f) and P(f) the ω-limit set and the set of periodic points of f, respectively. It is well known that for an interval map f, the following statements hold: (1) If P(f) = {x: f(x) = x}, then for any nonempty connected subset Aof [0, 1], the topological limit of trajectory of Aunder fexists. (2) If x∈ ω(f) - P(f), then the orbit O(x, f) of xunder fis an infinite set. The aim of this note is to show that the above statements do not hold for dendrite maps.

Co-precipitation reaction soft chemistry method was employed to prepare fine YPO4:Eu3+ phosphor particles calcined at different temperature. Adjusting appropriate pH and introducing lithium may greatly affect the particle size of the sample and further affect the luminescence intensity. The as-prepared samples were characterized by X-ray diffraction (XRD), transmission electron micrograph (TEM) and photoluminescence (PL) spectroscopy. The XRD patterns of YPO4:Eu3+ have only peaks of tetragonal xenotime and the sizes of particles range from 8 to 12 nm without Li2CO3 flux. The addition of Li2CO3 flux to precursor leads to a morphological modification for both the shape and size of the final phosphor, further affect the luminescence intensity. From the fluorescence spectra the emission transition 5D0 → 7F1 is more prominent than the normal red emission transition (5D0 → 7F2). (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)