Coincidence of length spectra does not imply isospectrality
Fulling, S. A. ; Kuchment, Peter
arXiv, 0505200 / Harvested from arXiv
Text on arXiv
Penrose--Lifshits mushrooms are planar domains coming in nonisometric pairs with the same geodesic length spectrum. Recently S. 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.
Publié le : 2005-05-10
Classification:  Mathematics - Spectral Theory,  Mathematical Physics,  Mathematics - Analysis of PDEs 
@article{0505200,
     author = {Fulling, S. A. and Kuchment, Peter},
     title = {Coincidence of length spectra does not imply isospectrality},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0505200}
}

Fulling, S. A.; Kuchment, Peter. Coincidence of length spectra does not imply isospectrality. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0505200/