Descripción: Recent experimental and theoretical methods allowed the efficient investigation of highly excited rovibrational states of molecular systems. At these levels of excitation the correspondence principle holds, and then classical mechanics can provide intuitive views of the involved processes. In this respect, we have recently shown that for completely hyperbolic systems, homoclinic motions, which are known to organize the classical chaotic region in Hamiltonian systems, imprint a clear signature in the corresponding highly excited quantum spectra. In this Communication we show that this result also holds in mixed systems, by considering an application to the floppy LiNCLiCN molecular system. © 2005 American Institute of Physics.

Descripción: In this paper we introduce the generalized eigenvalues of a quasilinear elliptic system of resonant type. We prove the existence of infinitely many continuous eigencurves, which are obtained by variational methods. For the one-dimensional problem, we obtain an hyperbolic type function defining a region which contains all the generalized eigenvalues (variational or not), and the proof is based on a suitable generalization of Lyapunov's inequality for systems of ordinary differential equations. We also obtain a family of curves bounding by above the kth variational eigencurve. © 2006 Elsevier Inc. All rights reserved.