New York Journal of Mathematics
Volume 21 (2015) 163-180


V. Guillemin, A. Uribe, and Z. Wang

Canonical forms for perturbations of the harmonic oscillator

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Published: March 2, 2015
Keywords: Harmonic oscillator, toric sysem, Birkhoff canonical form
Subject: 35P20, 37J40

We consider a class of perturbations of the 2D harmonic oscillator, and of some other dynamical systems, which we show are isomorphic to a function of a toric system (a Birkhoff canonical form). We show that for such systems there exists a quantum normal form as well, which is determined by spectral data.


V. Guillemin is supported in part by NSF grant DMS-1005696.
A. Uribe is supported in part by NSF grant DMS-0805878.

Author information

V. Guillemin:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

A. Uribe:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA

Z. Wang:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhi, 230026, China