Coincidence of length spectra does not imply isospectrality Academic Article

abstract

• Penrose-Lifshits mushrooms are planar domains coming in nonisometric pairs with the same geodesic length spectrum. Recently Zelditch raised the question whether such billiards also have the same eigenvalue spectrum for the Dirichlet Laplacian (conjecturing 'no'). Here we show that generically (in the class of smooth domains) the two members of a mushroom pair have different spectra. 2005 IOP Publishing Ltd.

authors

• Kuchment, Peter

published proceedings

• INVERSE PROBLEMS

author list (cited authors)

• Fulling, S. A., & Kuchment, P.

citation count

• 3

complete list of authors

• Fulling, SA||Kuchment, P

publication date

• August 2005

publisher

• IOP Publishing  Publisher

published in

• Inverse Problems  Journal

keywords

• 49 Mathematical Sciences
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1088/0266-5611/21/4/013

start page

• 1391

end page

• 1395

volume

• 21

issue

• 4

URL

• http://dx.doi.org/10.1088/0266-5611/21/4/013