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Topic: Isospectral

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	PlanetMath: isospectral
		Two linear operators are said to be isospectral or cospectral if they have the same spectrum.
		This is version 2 of isospectral, born on 2004-10-17, modified 2004-10-23.
		Object id is 6387, canonical name is Isospectral.
	planetmath.org /encyclopedia/Cospectral.html (65 words)

	Some planar isospectral domains
		In the ensuing 25 years many examples of isospectral manifolds were found, whose dimensions, topology, and curvature properties gradually approached those of the plane.
		The isospectral subgroups A and B are the point-stabilizers in these two permutation representations.
		Deforming the metric on this 23-fold cross surface by replacing its hyperbolic triangles by scalene Euclidean triangles yields a cone-manifold M whose quotients by A and B are non-congruent planar isospectral domains.
	www.math.dartmouth.edu /~doyle/docs/drum/drum/drum.html (1834 words)

	Isospectral Metrics On Five-Dimensional Spheres (ResearchIndex) (Site not responding. Last check: 2007-11-04)
		We construct isospectral pairs of Riemannian metrics on S 5 and on B 6, thus lowering by three the minimal dimension of spheres and balls on which such metrics have been constructed previously (S n8 and B n9).
		We also construct continuous families of isospectral Riemannian metrics on S 7 and on B 8.
		2 A new construction of isospectral Riemannian nilmanifolds wi..
	citeseer.ist.psu.edu /449107.html (404 words)

	Content of JGA
		The purpose of this paper is to present the first continuous families of Riemannian manifolds that are isospectral on functions but not on I -forms, and, simultaneously, the first continuous families of Riemannian manifolds with the same marked length spectrum but not the same 1-form spectrum.
		Examples of isospectral manifolds that are not isospectral on forms are sparse, as most examples of isospectral manifolds can be explained by Sunada's method or its generalizations, hence are strongly isospectrul.
		Isospectral manifolds constructed using the Gordon-Wilson method, a generalized Sunada method, are strongly isospectral and must have the same marked length spectrum.
	www.jga.wustl.edu /contents/v10n2/abstract.html (848 words)

	NSF-CBMS Regional Conference in the Mathematical Sciences: "Advances in Inverse Spectral Geometry" Abstract
		Examples include, among others, isospectral deformations arising from the representation theoretic techniques of Lecture 3, new examples of isospectral deformations constructed by R. Gornet by different methods, and isospectral nilmanifolds with different local geometry (to be discussed in lecture 8).
		We exhibit a pair of flat bordered surfaces which are isospectral for the Neumann boundary conditions, one of which is orientable while the other is nonorientable.
		The surfaces are constructed using the orbifold version of Sunada's theorem, and Neumann isospectrality is verified explicitly by transplantation of eigenfunctions.
	www.math.ttu.edu /current/cbms1996/abstract.html (1059 words)

	Generating Functions for Point Set Distances (Site not responding. Last check: 2007-11-04)
		The smallest isospectral pairs in the first few bases are shown below (as decimal numbers) 2 {2375,2755} 3 {935,1199} 4 {414,486} 5 {814,1342} Again this raises the question of whether the numerical relation XX'=YY' for any particular base is sufficient as well as necesary for X and Y to be isospectral.
		Incidentally, the existence of distinct isospectral arrangements of points in one-dimensional space can also be expressed in terms of a combinatorial proposition involving sequences of integers.
		A application of generating functions to higher dimensional configurations is discussed in Isospectral Point Sets in Higher Dimensions.
	www.mathpages.com /home/kmath390.htm (1870 words)

	Some planar isospectral domains
		In the ensuing 25 years many examples of isospectral manifolds were found, whose dimensions, topology, and curvature properties gradually approached those of the plane.
		yields a simplified version of the pair of isospectral domains given by Gordon, Webb, and Wolpert [5], [4], which was obtained by bisecting a pair of flat but non-planar isospectral domains given earlier by Buser [2].
		Deforming the metric on this 23-fold cross surface by replacing its hyperbolic triangles by scalene Euclidean triangles yields a cone-manifold M whose quotients by A and B are non-congruent planar isospectral domains.
	math.dartmouth.edu /~doyle/docs/drum/drum/drum.html (1834 words)

	Isospectral Point Sets In Higher Dimensions (Site not responding. Last check: 2007-11-04)
		It’s possible for geometrically distinct arrangements of particles to have the same distance spectrum, in which case the arrangements are said to be isospectral.
		One-dimensional isospectral configurations are discussed in Generating Functions for Point Set Distances.
		To confirm that these three configurations are isospectral we need only show that their indicator polynomials are identical.
	www.mathpages.com /home/kmath076/kmath076.htm (1221 words)

	Isospectral Potentials and Conformally Equivalent Isospectral Metrics on Spheres, Balls and Lie Groups (ResearchIndex)
		Isospectral Potentials and Conformally Equivalent Isospectral Metrics on Spheres, Balls and Lie Groups
		Abstract: We construct pairs of conformally equivalent isospectral Riemannian metrics '1 g and '2 g on spheres S and balls B n+1 for certain dimensions n, the smallest of which is n = 7, and on certain compact simple Lie groups.
		3 On manifolds of negative curvature with isospectral potentia..
	citeseer.ist.psu.edu /605325.html (648 words)

	Isospectral - Wikpedia (Site not responding. Last check: 2007-11-04)
		In mathematics, two linear operators are called isospectral if they have the same spectrum.
		In the case of operators on infinite-dimensional spaces, the spectrum need not consist solely of isolated eigenvalues; the rest of this article will assume for clarity that we are talking about operators on finite-dimensional vector spaces.
		In that case, for complex square matrices, the relation of being isospectral for two diagonalizable matrices is just similarity.
	www.bostoncoop.net /~tpryor/wiki/index.php?title=Isospectral (217 words)

	About "Some Planar Isospectral Domains" (Site not responding. Last check: 2007-11-04)
		A paper on isospectral pairs of plane domains, and a particularly simple method of proving isospectrality.
		One example is a pair of domains that are not only isospectral but homophonic, showing that one really can't hear the shape of a drum.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.org /library/view/5211.html (68 words)

	Isospectral Flows and Nonholonomic Stabilization by Anthony Bloch, University of Michigan
		Isospectral Flows and Nonholonomic Stabilization by Anthony Bloch, University of Michigan
		Nonholonomic systems are not stabilizable by smooth feedback and I will present an algorithm which uses discrete switching between smooth flows.
		The switching is essentially between flows which preserve eigenvalues of matrices (isospectral flows, similar to those found in the theory of integrable systems), and certain double bracket flows, similar to those found in gradient systems theory.
	www.ima.umn.edu /dynsys/wkshp_abstracts/bloch1.html (169 words)

	Isospectral Manifolds (Site not responding. Last check: 2007-11-04)
		This article aims at constructing nonisometric, isospectral manifolds modelled on semisimple Lie groups with finite center and no compact factors.
		Our two main results are the construction of arbitrarily large sets of closed, isospectral, nonisometric manifolds and pairs of infinite towers of finite covers that are isospectral and nonisometric at each stage.
		We also show the growth of these large sets of isospectral manifolds as a function of volume is super-polynomial.
	www.ma.utexas.edu /~dmcreyn/Isospectral.html (98 words)

	Abstract Display for Eigenmodes of Isospectral Drums (Site not responding. Last check: 2007-11-04)
		That is, one cannot "hear the shape of a drum." All known examples of such regions are bounded by polygons with reentrant corners.
		While the isospectrality can be proven mathematically, analytical techniques are unable to produce eigenvalues themselves.
		We describe an algorithm due to Descloux and Tolley that blends finite elements with domain decomposition, and show that, with a modification that doubles its accuracy, this algorithm can be used to compute efficiently the eigenvalues for polygonal regions.
	techreports.library.cornell.edu:8081 /Dienst/UI/1.0/Summarize/cul.tc/95-209 (158 words)

	Division Algebras and Isospectral Manifold
		Two compact Riemanian manifolds are said to be isospectral if the (multi-set of) the eigenvalues of their Laplacians are equal.
		The question of finding isospectral non-isometric manifolds has a long history starting with Marc Kac's seminal paper (1966): " Can you hear the shape of a drum?" Various methods are known to construct such manifolds- the most powerful is due to Sunada.
		For locally symetric manifolds M (i.e., M= D\G/K, G semisimple Lie groups, K maximal compact subgroup and D a lattice in G) all the know examples are commensurable to each other.
	www.math.yale.edu /calendar/event.php?ID=350&Date=2005-03-23 (175 words)

	Eigenmodes of Isospectral Drums (Site not responding. Last check: 2007-11-04)
		That is, one cannot "hear the shape of a drum." The simplest isospectral regions known are bounded by polygons with reentrant corners.
		While the isospectrality can be proven mathematically, analytical techniques are unable to produce the eigenvalues themselves.
		We present results accurate to 12 digits for the most famous pair of isospectral drums, as well as results for another pair.
	epubs.siam.org /sam-bin/dbq/article/28506 (198 words)

	IngentaConnect Spectral Properties of Four-Dimensional Compact Flat Manifolds (Site not responding. Last check: 2007-11-04)
		We study the spectral properties of a large class of compact flat Riemannian manifolds of dimension 4, namely, those whose corresponding Bieberbach groups have the canonical lattice as translation lattice.
		By using the explicit expression of the heat trace of the Laplacian acting on p-forms, we determine all p-isospectral and L-isospectral pairs and we show that in this class of manifolds, isospectrality on functions and isospectrality on p-forms for all values of p are equivalent to each other.
		with the same length multiplicities), showing that there are two weak length isospectral pairs that are not length isospectral, and many pairs, p-isospectral for all p and not length isospectral.
	www.ingentaconnect.com /content/klu/agag/2006/00000029/00000001/00001151 (209 words)

	The identification of a time dependent sorption parameter from soil column experiments (Site not responding. Last check: 2007-11-04)
		A connection is established via conformal maps between vibrating membranes that are isospectral with respect to shape and those that are isospectral with respect to density.
		In particular, inhomogeneous circular membranes are constructed that are isospectral to polygonal membranes of uniform density via the Schwarz–Christoffel mapping.
		Although some corners of the polygons lead to singularities in the constructed densities, the densities are shown to be integrable.
	campus.murraystate.edu /academic/faculty/maeve.mccarthy/abstracts/knowlesmccarthy.html (87 words)

	12.3.3 Isospectral drums (Site not responding. Last check: 2007-11-04)
		The answer is negative, in that examples have been found for drums with different shapes but identical spectra.
		Here we present eigenvalue calculations for a pair of isospectral drums analysed by Driscoll.
		These mesh files are straightforward; they prescribe a pair of 8-sided quadrilaterals with re-entrant corners.
	www.ualberta.ca /AICT/RESEARCH/NAG/FastfloDoc/Tutorial/html/node107.html (212 words)

	Annals of Mathematics, II. Series, Vol. 149, No. 1, pp. 287-308, 1999 (Site not responding. Last check: 2007-11-04)
		This paper continues interesting work done by a number of authors on constructions of continuous families of isospectral metrics on compact Riemannian manifolds, that is, isospectral deformations of Riemannian metrics, which are not isometric.
		In this paper the author obtains similar results by considering isospectral deformations on the product $S^n\times S,$ where $S$ is a compact simply connected Lie group, in particular on $S^n\times S^3\times S^3$, and then embedding the nonsimply connected torus in $S$ and extending the metrics in such a way as to preserve the isospectrality.
		The nonisometry of the metrics is reflected either by different critical values of the scalar curvature function or by changes in the heat invariants for the Laplacian on 1-forms under the deformations.
	www.zblmath.fiz-karlsruhe.de /exx/journals/Annals/149_1/9.html (243 words)

	[No title] (Site not responding. Last check: 2007-11-04)
		Abstract : After briefly overviewing the history of isospectral, non-isometric manifolds we focus on isospectral manifolds which are not even locally isometric.
		All of the explicit examples which were known until now had in common that they involved 2-step nilpotent Lie groups, endowed with a left invariant metric, whose Lie algebras satisfied a certain isospectrality condition.
		The isospectral manifolds then basically arose as either submanifolds or quotients of these groups.
	www.math.technion.ac.il /~techm/19990614153019990614sch (186 words)

	Eigenmodes of isospectral drums
		You can obtain a copy of "Eigenmodes of isospectral drums," which appeared in the March 1997 SIAM Review.
		You can see more examples of isospectral regions in this paper by Buser, Conway, Doyle, and Semmler.
		They also produce a pair of "homophonic" drums: each has a special point at which the corresponding normalized eigenfunctions have identical values.
	www.math.udel.edu /~driscoll/research/drums.html (606 words)

	Gordon, Gornet, Schueth, Webb, ...: Isospectral deformations of closed riemannian manifolds with different scalar ...
		We construct the first examples of continuous families of isospectral Riemannian metrics that are not locally isometric on closed manifolds, more precisely, on
		GORDON, Isospectral deformations I: Riemannian structures on two-step nilspaces, Comm.
		SCHUETH, Isospectral deformations on Riemannian manifolds which are diffeomorphic to compact Heisenberg manifolds, Comment.
	www-mathdoc.ujf-grenoble.fr /numdam-bin/item?id=AIF_1998__48_2_593_0 (374 words)

	Atlas: Isospectral Lie groups and isospectral spheres by Dorothee Schueth (Site not responding. Last check: 2007-11-04)
		In order to detect local geometric properties which are not spectrally determined one needs examples of isospectral manifolds which are not locally isometric.
		We give a useful reformulation in terms of connection forms and apply this to construct the first examples of left invariant isospectral metrics on compact Lie groups.
		A local property in which these isospectral metrics differ from each other is the norm of the Ricci tensor.
	atlas-conferences.com /c/a/f/v/89.htm (173 words)

	Isospectral deformations of commutative spectral triples
		We are now ready to exhibit the isospectral deformation of the standard commutative example for a spin manifold
		The deformation is called isospectral for the simple reason that the operator
		In conclusion: the isospectral deformation procedure of Connes and Landi yields a family of noncommutative spectral triples that satisfy all of our stated conditions for a noncommutative spin geometry.
	www.mimuw.edu.pl /~pwit/TOK/sem3/online/node55.html (409 words)

	IngentaConnect Transformations between isospectral membranes yield conformal map... (Site not responding. Last check: 2007-11-04)
		IngentaConnect Transformations between isospectral membranes yield conformal map...
		In two dimensions, contrary to the known situation that a conformal transformation yields isospectral density functions for vibrating membranes, it is shown that a coordinate transformation leading to isospectral densities must be conformal.
		You will be able to remove this item from your shopping cart at any time before you have completed check-out.
	www.ingentaconnect.com /content/oup/imamat/2005/00000070/00000006/art00748 (101 words)

	Atlas: Generating Strictly Isospectral Systems via Structure Preserving Transformations by Uwe Prells (Site not responding. Last check: 2007-11-04)
		In this presentation we show how to generate strictly isospectral systems by applying structure preserving transformations to a linearization of a given system.
		D + K with nonsingular M and derive conditions on the parameters of the structure preserving transformations to ensure that in addition also symmetric (hermitian) coefficient matrices are preserved.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caow-87.
	atlas-conferences.com /cgi-bin/abstract/caow-87 (173 words)

	nlin.CD/0504050: Gnutzmann, Sven, Smilansky, Uzy, Sondergaard, Niels (Site not responding. Last check: 2007-11-04)
		Abstract: Several types of systems were put forward during the past decades to show that there exist {\it isospectral} systems which are {\it metrically} different.
		We propose that the spectral ambiguity can be resolved by comparing the nodal sequences (the numbers of nodal domains of eigenfunctions, arranged by increasing eigenvalues).
		In the case of isospectral flat tori in four dimensions - where a 4-parameters family of isospectral pairs is known- we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count.
	front.math.ucdavis.edu /nlin.CD/0504050 (236 words)

	Buser: Isospectral Riemann surfaces
		We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian.
		In a second part we give examples of isospectral non isometric surfaces in
		URAKAWA, Bounded domains which are isospectral but not congruent, Ann.
	www-mathdoc.ujf-grenoble.fr /numdam-bin/item?id=AIF_1986__36_2_167_0 (259 words)

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