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Topic: Monodromy

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	Monodromy - Wikipedia, the free encyclopedia
		In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology and differential geometry behave as they 'run round' a singularity.
		It is closely associated with covering maps and their degeneration into ramification; the aspect giving rise to monodromy phenomena is that certain functions we may wish to define fail to be single-valued as we 'run round' a path encircling a singularity.
		In this case the monodromy group is infinite cyclic and the covering space is the universal cover of the punctured complex plane.
	en.wikipedia.org /wiki/Monodromy (697 words)

	Monodromy
		The concept of monodromy was first introduced in 1980 by J.J. Duistermaat in the context of classical mechanics, as the basic topological obstruction to the existence of global action-angle variables in integrable Hamiltonian systems.
		Monodromy is instead cancelled whenever the isomerization pathway has a waist, as is the case for HCN-CNH.
		Then, we again applied Canonical Perturbation Theory to an ab initio surface for CO and showed that this molecule displays monodromy in the 3-dimensional space of the symmetric CO stretch, the bend, and the vibrational angular momentum, which are coupled by a strong 2:1:1 Fermi resonance.
	www-lsp.ujf-grenoble.fr /recherche/a2t1/a2t1a3/dynamique/joyeux/monodromy.htm (478 words)

	The Monodromy Pairing (Site not responding. Last check: 2007-09-20)
		The monodromy pairing is a nondegenerate (imperfect) Hecke-equivariant integer-valued pairing on the module of supersingular points.
		This pairing is diagonal with respect to the basis of enhanced supersingular elliptic curves, and the pairing of an enhanced curve with itself is half the number of automorphisms of that enhanced curve.
		This gives rise to a nontrivial monodromy pairing on the supersingular module, which we demonstrate for p = 23 --- note that j = 12^3 = 3 mod 23.
	www.umich.edu /~gpcc/scs/magma/text1136.htm (198 words)

	PlanetMath: monodromy
		Definition 2 The action described in the above theorem is called the monodromy action and the corresponding homomorphism
		This is version 5 of monodromy, born on 2003-02-08, modified 2004-02-18.
		Object id is 4000, canonical name is Monodromy.
	planetmath.org /encyclopedia/Monodromy2.html (175 words)

	INI : Abstracts : GMR : Integrable reductions of Einstein's field equations: monodromy transform and the linear ... (Site not responding. Last check: 2007-09-20)
		These set of functions arises as the monodromy data for the fundamental solution of associated linear systems (``spectral problems'') and they can serve as free independent ``coordinates'' in the infinite dimensional space of the local solutions.
		In principle, the monodromy data functions can be calcul ated also from some boundary, or initial, or characteristic initial data for the fields, and many physical properties of solutions are simply ``encoded'' in the analytical structures of these functions.
		The structure of the direct problem of the monodromy transform and general construction of the linear singular integral equation solving the inverse problem will be considered and some applications of this approach for construction of infinite hierarchies of exact solutions will be presented.
	www.newton.cam.ac.uk /programmes/GMR/alekseev.html (301 words)

	[No title]
		Given a periodic orbit at a particular energy or period, the monodromy method is a way of computing another periodic orbit (usually in the same family) at a nearby energy or period.
		Using the monodromy method with fixed energies, it was possible to move down the orbit to the branching point, at which point one could move horizontally to the other orbit by using the monodromy method with fixed periods.
		For each energy, the monodromy method (operating at fixed energy) was used to compute the orbits in each family at that energy, along with their periods and monodromy matrices.
	www.mit.edu /~stevenj/Thesis/Thesis.html (3397 words)

	Non-Hamiltonian monodromy - Cushman, Duistermaat (ResearchIndex) (Site not responding. Last check: 2007-09-20)
		This can be used to prove that nontrivial monodromy occurs in the two best known integrable cases of rolling bodies: the heavy solid of revolution rolling on a...
		Loosely speaking, if an integrable system has monodromy then it is impossible to label the tori in a unique way by values of the...
		Monodromy in the Resonant Swing Spring - Dullin, Giacobbe, Cushman (2002)
	citeseer.ist.psu.edu /66833.html (534 words)

	[No title]
		The monodromy m.i of branchpoint b.i is the permutation of L one obtains by applying analytic continuation on L following a path from x0 to b.i, going around b.i counter clockwise, and returning to x0.
		If the optional argument group is given then the output will be the monodromy group G, the permutation group generated by the m.i.
		It determines the monodromy by analytic continuation (using Maple's fsolve).
	www.math.fsu.edu /~hoeij/periodmatrix/help_pages (1351 words)

	Research (Site not responding. Last check: 2007-09-20)
		As many questions that we addressed were motivated by the need to classify hyper-surfaces in algebraic geometry, which can be done sometimes, and among other methods, using the braid monodromy, and the computation of the fundamental group of the complement of a given branch curve of a hyper-surface.
		The paper "Computing Braid Monodromy for Plane Algebraic Curves" connects known methods for computing braid monodromy using the polynomial defining the curve with the Moishezon-Teicher algorithm, in order to maintain the simplicity of the Moishezon-Teicher algorithm while performing computations for a larger class of plane curves.
		The generalized algorithms for computing braid monodromy together with the algorithms for solving the braid word problem may be used together as an automated method to compute the fundamental group of the complement of a given curve.
	www.cs.biu.ac.il /~kaplansh/research.htm (1233 words)

	Monodromy (Site not responding. Last check: 2007-09-20)
		In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology and differential geometry behave as they 'run
		Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds...
		The concept of monodromy was first introduced in 1980 by J.J. Duistermaat in the context of classical mechanics, as the basic topological obstruction
	www.monodromy.info (245 words)

	Mathematics
		The integral monodromy of hyperelliptic and trielliptic curves
		We prove that the Z/l monodromy of the moduli space of trielliptic curves with signature $(r,s)$ is a special unitary group.
		That is, the image of monodromy in slope s, necessarily a subgroup of the units of the division algebra of invariant s, has finite index.
	www.math.colostate.edu /~achter/math.html (1162 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		The monodromy of the classical analogue of this problem is studied in Dullin et al.
		The form of the monodromy matrix is obtained from the lattice of quantum states and depends on the choice of an elementary cell of the lattice.
		We compute the quantum monodromy matrix, that is the inverse transpose of the classical monodromy matrix.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20606529 (303 words)

	Katz, N.M.: Twisted L-Functions and Monodromy. (AM-150).
		The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves.
		The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy.
		Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.
	pup.princeton.edu /titles/7234.html (258 words)

	Non-abelian unipotent periods Monodromy of iterated integrals (Site not responding. Last check: 2007-09-20)
		Non-abelian unipotent periods Monodromy of iterated integrals, by Zdzislaw Wojtkowiak
		Their calculations reduce to calculations of the monodromy of iterated integrals on algebraic varieties.
		We study the monodromy with some details on pointed projective lines and on configuration spaces.
	www.math.uiuc.edu /K-theory/0017/index.html.old (82 words)

	Proceedings of the American Mathematical Society
		Hurwitz monodromy, spin separation and higher levels of a modular tower, Arithmetic fundamental groups and noncommutative algebra, editors M. Fried and Y. Ihara, 79-220, Proc.
		Monodromy groups of branched coverings: the generic case, Recent developments of the inverse Galois problem (Seattle, Wa, 1993), Contemp.
		The monodromy group of a function on a general curve, Israel J. Math., to appear.
	www.mathaware.org /proc/2005-133-02/S0002-9939-04-07713-5/home.html (394 words)

	p-adic monodromy of the ordinary locus of Picard moduli scheme
		p-adic monodromy of the ordinary locus of Picard moduli scheme
		The naive p-adic monodromy of the ordinary locus of the good reduction of a Shimura variety of U(m, n) type over $F p$ is a subgroup of GL
		From this local information, the global p-adic monodromy is shown to be as big as possible, i.e.
	repository.upenn.edu /dissertations/AAI3165802 (152 words)

	Monodromy of Polylogarithms (ResearchIndex) (Site not responding. Last check: 2007-09-20)
		We calculate the monodromy at the two singularities.
		As opposed to the classical polylogs [11, 12], the monodromy of generalized polylogs involves the so-called "multiple zeta values," [14] which play an important role in number theory, knot theory [4, 6, 5, 10], and physics [7, 9].
		Via monodromy of polylogs, Radford [13] showed that the C-algebra of polylogs is isomorphic to the C-algebra of...
	citeseer.ist.psu.edu /402872.html (166 words)

	18.937 - Topics in Geometric Topology - Spring 2006 (Site not responding. Last check: 2007-09-20)
		Mon Apr 24: braid monodromy for projective curves; monodromy factorizations, Hurwitz equivalence; Hurwitz curves.
		Wed May 3: the Zariski-Van Kampen theorem; symmetric group monodromy, Chisini conjecture; examples of braid monodromies.
		Mon May 15: Lefschetz pencils and their monodromy; the pencil of conics on CP^2; Gompf and Donaldson's theorems; pencils vs. branched covers: lifting the monodromy
	www-math.mit.edu /~auroux/18.937 (497 words)

	First experimental evidence of quantum monodromy
		The effect, called quantum monodromy (Greek for "once around"), relates in part to the behavior of molecules based on their atomic structure and vibrational frequencies.
		A better understanding of quantum monodromy could have implications in astronomy, atmospheric science, and biology.
		For molecules that exhibit quantum monodromy, the map looks like an upright cylinder with a bulge rising from the bottom, like the bottom of a wine or champagne bottle.
	www.eurekalert.org /pub_releases/2005-06/osu-fee062005.php (560 words)

	www.monodromy.com
		This site is devoted to monodromy in all its incarnations, classical and l-adic, local and global, arithmethic and geometric.
		If not, it is almost certainly because you are aware, at some level, of your personal monodromy.
		Think how much richer and more fulfilling life would be if you were completely aware of all the monodromy which surrounds you.
	www.monodromy.com (132 words)

	The Monodromy Group - Wal-Mart
		In singularity theory and algebraic geometry the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations.
		On the other hand, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions.
		The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers.
	www.walmart.com /catalog/product.gsp?product_id=4974882 (642 words)

	Monodromy matrix - Wikipedia, the free encyclopedia
		In mathematics, and particularly ordinary differential equations, a monodromy matrix is the inverse of the fundamental matrix of a system of ODEs evaluated at zero times the fundamental matrix evaluated at the period of the coefficients of the system.
		Examples of finding the monodromy matrix of systems of ODEs from www.exampleproblems.com.
		This page was last modified 22:17, 1 April 2006.
	en.wikipedia.org /wiki/Monodromy_matrix (83 words)

	the monodromy principle
		It should not be thought that bypassing a singularity by two routes should always give the same result; but two routes which don't surround a singularity must.
		This is the monodromy theoremmonodromy theorem; the process is called analytic continuationanalytic continuation.
		Sometimes an attempt at continuation will strike a barrier, no matter what route is taken.
	delta.cs.cinvestav.mx /~mcintosh/comun/complex/node30.html (342 words)

	Monodromy of Polylogarithms
		Here, monodromy is used to give an induction proof of the linear independence of the polylogarithms.
		We also obtain a Gröbner basis of the polynomial relations between ``multiple zeta values'' using the techniques of non-commutative algebra.
		To compute the monodromy, we use the standard keyhole contours about the two singularities z=0 and z=1.
	algo.inria.fr /seminars/sem97-98/minh.html (771 words)

	INI Programme PEM Workshop - Painlevé Equations and Monodromy Problems: An Introduction (Site not responding. Last check: 2007-09-20)
		This workshop will give an introduction to Painlevé equations and monodromy problems suitable for postgraduate students and postdoctoral researchers.
		Invited participants to the Painlevé Equations and Monodromy Problems programme whose dates coincide with those of the workshop need not apply or pay any registration fee.
		The closing date for the receipt of applications has passed, however late applications may still be considered.
	www.newton.cam.ac.uk /programmes/PEM/pemw01.html (233 words)

	Monodromy and Gauß-Manin connection
		The Gauß-Manin connection may be considered as an algebraic description of the monodromy action by means of differential forms.
		The first important theorem is the monodromy theorem, due to Deligne in the global and to Brieskorn in the local situation which says that the eigenvalues of
		It is a fundamental fact that the Picard-Lefschetz monodromy
	www.mathematik.uni-kl.de /~zca/Reports_on_ca/30/paper_html/node2.html (752 words)

	Quantum monodromy in the two-centre problem
		Using modern tools from the geometric theory of Hamiltonian systems it is shown that electronic excitations in diatoms which can be modelled by the two-centre problem exhibit a complicated case of classical and quantum monodromy.
		The asymmetric case has a non-local singularity causing monodromy.
		An interpretation of monodromy is given in terms of the caustics of invariant tori.
	stacks.iop.org /0305-4470/36/L307 (274 words)

	Amazon.com: Random Matrices, Frobenius Eigenvalues, and Monodromy (Colloquium Publications (Amer Mathematical Soc)): ... (Site not responding. Last check: 2007-09-20)
		This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields.
		The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.
		SIPs: inequality discrep, geometric monodromy group, corresponding separation vector, proper smooth family, irreducible nontrivial representation (more)
	www.amazon.com /exec/obidos/tg/detail/-/0821810170?v=glance (572 words)

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