A geometric criterion for positive topological entropy

We prove that a diffeomorphism possessing a homoclinic point with a topological crossing (possibly with infinite order contact) has positive topological entropy, along with an analogous statement for heteroclinic points. We apply these results to study area-preserving perturbations of area-preserving surface diffeomorphisms possessing homoclinic and double heteroclinic connections. In the heteroclinic case, the perturbed map can fail to have positive topological entropy only if the perturbation preserves the double heteroclinic connection or if it creates a homoclinic connection. In the homoclinic case, the perturbed map can fail to have positive topological entropy only if the perturbation preserves the connection. These results significantly simplify the application of the Poincaré-Arnold-Melnikov-Sotomayor method. The results apply even when the contraction and expansion at the fixed point is subexponential.The first author was partially supported by a Sloan Foundation Fellowship and an N.S.F. grant. The second author was partially supported by a National Science Foundation Postdoctoral Research Fellowship. Both authors would like to thank MSRI for their support during the period that much of this paper was written.     

Index of refraction in ‘dirty’ displacive ferroelectrics

We report measurements of the optic index of reflection as a function of temperature, n(T), for several highly disordered ferroelectrics: PLZT ceramic [Pb_1?xLa_x(Zr_0.65Ti_0.35)_1?x/4O₃ where x = 0.08] and single crystals of Pb₃(MNb₂)O₉ where M = Zn and Mg. The results are qualitatively different from the unusual displacive ferroelectric behavior and the difference is clearly due to local disorder.     

Studies in qualitative inorganic analysis. Part XXI

Summary Interference with the lead plate test for fluoride by borate and fluoborate can be eliminated by applying tests for silica and borate to the water drop, these tests allowing positive identification of the presence of silica and borate in the sample.

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Zusammenfassung Die durch Borat und Fluoborat verursachte Störung des Fluoridnachweises nach dem Bleiplattenverfahren läßt sich durch Prüfung auf Kieselerde und Borat im Wassertropfen vermeiden, deren Anwesenheit in der Probe hiermit eindeutig feststellbar ist.

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Résumé On peut éliminer l'interférence des fluorures avec les borates et les fluoborates dans l'essai à la lame de plomb en effectuant la recherche de la silice et des borates sur une goutte d'eau, ce qui permet l'identification positive de la présence de silice et de borate dans l'échantillon.

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Part XX: Mikrochim. Acta [Wien]1964, 790.     

Passive stabilization of a passively mode-locked laser by nonlinear absorption in indium phosphide

A diode-pumped Nd:KGd(WO4)2 laser mode locked by a saturable Bragg reflector (SBR) is passively stabilized to suppress Q-switched mode locking and to extend the parameter range of continuous-wave mode locking. An indium phosphide plate exhibiting two-photon absorption and free-carrier absorption is used for passive stabilization. The intracavity pulse energy for the onset of stable continuous-wave mode locking is reduced by a factor of 4 compared with the laser without stabilization. By increasing the modulation depth of the SBR, pulse shortening by 30% is achieved and bandwidth-limited 6.2-ps pulses are measured.     

Electron localization and superconductivity in very thin epitaxially grown Ag films on Ge (001)

Transport properties of very thin (2.5 monolayer) films of Ag epitaxially grown on clean Ge (001) substrates are reported. The films consist of a monolayer coverage plus isolated three dimensional islands. Below ～70°K the conductivity is dominated by the metal film and displays the temperature and electric and magnetic field dependences characteristic of metallic weak localization in two dimensions. Below ～2°K the resistance drops rapidly in a manner resembling an incomplete superconducting transition. The resistance is restored by application of a magnetic field of ～20 KGauss at 0.6°K.