Resonances for homoclinic trapped sets / Jean-François Bony, Setsuro Fujiié, Thierry Ramond, Maher Zerzeri.

Format:

Book

Author/Creator:

Bony, Jean-François, author.

Fujiie, Setsurō, author.

Ramond, Thierry, author.

Zerzeri, Maher, author.

Series:

Astérisque ; 405.

Astérisque, 0303-1179 ; 405

Language:

English

French

Subjects (All):

Schrödinger operator.

Dynamics.

Asymptotes.

Microlocal analysis.

Quantum theory--Mathematical models.

Resonance.

Physical Description:

vii, 314 pages : illustrations ; 24 cm.

Place of Publication:

Paris : Société Mathématique de France, 2018.

Language Note:

Abstract also in French.

Summary:

"We study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, we prove that there is no resonance in a region below the real axis. Then, we obtain a quantization rule and the asymptotic expansion of the resonances when there is a finite number of homoclinic trajectories. The same kind of results is proved for homoclinic sets of maximal dimension. Next, we generalize to the case of homoclinic/heteroclinic trajectories and we study the three bump case. In all these settings, the resonances may either accumulate on curves or form clouds. We also describe the corresponding resonant states"--Page 4 of cover.

Contents:

General setting

Resonance free domains

Asymptotic of the resonances generated by a finite number of homoclinic trajectories

Asymptotic of the resonences generated by nappes of homoclinic trajectories

Generalization to multiple barriers

Resonant states

General reduction

Proof of theorem 3.2

Proof of theorem 3.8

Proof of the asymptotic of the resonances for a finite number of homoclinic curves

Proof of the other results of Chapter 4

Proof of the asymptotic of the resonances for a nappe of homoclinic curves

Proof of the main results of Chapter 6

Proof of the other results of Chapter 6

Proof of the asymptotic of the resonant states

Review of semiclassical analysis

Some properties of the Hamiltonian flow

Spectral radius of [T] and [T]

Distorted and truncated estimates

Semiclassical maximum principle.

Notes:

Includes bibliographical references (pages 307-314).

ISBN:

9782856298947

285629894X

OCLC:

1082267144