Time-periodic perturbations of an asymmetric Duffing-Van-der-Pol equation close to an integrable equation with a homoclinic figure-eight of a saddle are considered. The behavior of solutions outside the neighborhood of figure-eight is studied analyti
cally. The problem of limit cycles for an autonomous equation is solved and resonance zones for a nonautonomous equation are analyzed. The behavior of the separatrices of a fixed saddle point of the Poincare map in the small neighborhood of the unperturbed figure-eight is ascertained. The results obtained are illustrated by numerical computations.
We report on the direct measurement of the electron-phonon relaxation time, {tau}eph, in disordered TiN films. Measured values of {tau}eph are from 5.5 ns to 88 ns in the 4.2 to 1.7 K temperature range and consistent with a T-3 temperature dependence
. The electronic density of states at the Fermi level N0 is estimated from measured material parameters. The presented results confirm that thin TiN films are promising candidate-materials for ultrasensitive superconducting detectors.
