Some examples of generalized reflectionless Schrödinger potentials

Russell Johnson; Luca  Zampogni

doi:10.3934/dcdss.2016046

Article Contents

2016, Volume 9, Issue 4: 1149-1170. Doi: 10.3934/dcdss.2016046

This issue Previous Article On the nonautonomous Hopf bifurcation problem Next Article Local study of a renormalization operator for 1D maps under quasiperiodic forcing

Some examples of generalized reflectionless Schrödinger potentials

Russell Johnson^1, and
Luca Zampogni^2,

1.
Dipartimento di Matematica e Informatica, Università di Firenze, Via di Santa Marta 3, 50139 Firenze
2.
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia

Received: May 2015

Revised: October 2015

Published: August 2016

Abstract / Introduction Related Papers Cited by

Abstract

the class of generalized reflectionless Schrödinger operators was introduced by Lundina in 1985. Marchenko worked out a useful parametrization of these potentials, and Kotani showed that each such potential is of Sato-Segal-Wilson type. Nevertheless the dynamics under translation of a generic generalized reflectionless potential is still not well understood. We give examples which show that certain dynamical anomalies can occur.

Keywords:

Generalized reflectionless potential,
reflectionless potential in the sense of Craig,
glueing property,
divisor map.

Mathematics Subject Classification: 37B55, 34B20, 34L40, 31A35.

Citation:

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