0 v 1 [ m at h . SP ] 1 1 M ay 2 00 5 Coincidence of length spectra does not imply isospectrality
نویسنده
چکیده
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.
منابع مشابه
ar X iv : 0 80 3 . 31 77 v 2 [ m at h . SP ] 1 5 M ay 2 00 8 LOCAL SPECTRAL PROPERTIES OF REFLECTIONLESS JACOBI , CMV , AND SCHRÖDINGER OPERATORS
We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely absolutely continuous spectrum on E.
متن کاملar X iv : 0 80 5 . 10 03 v 1 [ m at h . SP ] 7 M ay 2 00 8 GEODESICS ON WEIGHTED PROJECTIVE SPACES
We study the inverse spectral problem for weighted projective spaces using wave-trace methods. We show that in many cases one can “hear” the weights of a weighted projective space.
متن کاملar X iv : m at h / 04 11 14 0 v 2 [ m at h . N T ] 4 M ay 2 00 5 THE 3 x + 1 SEMIGROUP
The 3x + 1 semigroup is the multiplicative semigroup S of positive rational numbers generated by { 2k+1 3k+2 : k ≥ 0} together with {2}. This semigroup encodes backwards iteration under the 3x + 1 map, and the 3x + 1 conjecture implies that it contains every positive integer. This semigroup is proved to be the set of positive rationals a b in lowest terms with b 6≡ 0( mod 3), and so contains al...
متن کاملar X iv : 0 80 5 . 24 44 v 1 [ m at h . A G ] 1 6 M ay 2 00 8 Symmetry and holomorphy of the second member of the second Painlevé hierarchy
We study symmetry and holomorphy of the second member of the second Painlevé hierarchy P (2) II .
متن کاملar X iv : m at h / 00 12 25 1 v 2 [ m at h . A G ] 3 0 M ay 2 00 1 Euler Characteristics of Theta Divisors of Jacobians for Spectral Curves
We show how to calculate the Euler characteristic of an affine Jacobi variety of a spectral curve from its defining equations. 0 Membre du CNRS 1 Laboratoire associé au CNRS.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008