particularly ordinary differential equations (ODEs), a monodromy matrix is the fundamental matrix of a system of ODEs evaluated at the period of the coefficients...

In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave...

Y_{2}} defined near b. The new and old solutions are linked by the monodromy matrix Mi as follows: Y 2 = Y 1 M i . {\displaystyle Y_{2}=Y_{1}M_{i}.} One...

singularities (described by the monodromy matrix). The proof of the existence of such differential equations by previously known monodromy matrices is one of the...

complex quadratic mappings Characteristic multiplier, an eigenvalue of a monodromy matrix Multiplier algebra, a construction on C*-Algebras and similar structures...

distinct points (type I3), or all meet at the same point (type IV). The monodromy around each singular fiber is a well-defined conjugacy class in the group...

the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities...

of freedom and the other on the spin degrees of freedom produces a monodromy matrix whose determinant is directly proportional to S ^ 2 {\displaystyle...

differential equations, a characteristic multiplier is an eigenvalue of a monodromy matrix. The logarithm of a characteristic multiplier is also known as characteristic...

{\displaystyle \phi ^{-1}(0)\phi (T)} is known as the monodromy matrix. In addition, for each matrix B {\displaystyle B} (possibly complex) such that e T...

The difficulty in constructing global period mappings comes from the monodromy of B: There is no longer a unique homotopy class of diffeomorphisms relating...

monodromy representation of KZ equation with a general semi-simple Lie algebra agrees with the linear representation of braid group given by R-matrix...

theoretical questions include: asymptotic analysis; analytic continuation and monodromy in the complex plane; and symmetry principles and other structural equations...

known classically as Schwarz's list. In monodromy terms, the question is of identifying the cases of finite monodromy group. By reformulation and passing...

proof of the Weil conjectures. The Picard–Lefschetz formula describes the monodromy at a critical point. Suppose that f is a holomorphic map from an ⁠ ( k...

corresponds to the Yang–Baxter equation (see § Basic properties); and in monodromy invariants of algebraic geometry. In this introduction let n = 4; the...

order. Monodromy defects in non-trivial 2+1D SPT states carry non-trival statistics and fractional quantum numbers of the symmetry group. Monodromy defects...

boundary component. The monodromy map is then a homeomorphism of the 2-torus, which can be represented in this case by the matrix ( 2 1 1 1 ) {\displaystyle...

(2002)), can be stated as a Riemann–Hilbert problem. Likewise the inverse monodromy problem for Painlevé equations can be stated as a Riemann–Hilbert problem...

covered by an open subset of R n {\displaystyle {\mathbb {R} }^{n}} , with monodromy acting by affine transformations. This equivalence is an easy corollary...

-k-l&\gamma +l&z\\\alpha '+k&\beta '-k-l&\gamma '+l&\;\end{matrix}}\right\}} Method of Frobenius Monodromy Siklos, Stephen. "The Papperitz equation" (PDF). Archived...

& Sarnak, Peter (1999), Random matrices, Frobenius Eigenvalues, and Monodromy, Providence, RI: American Mathematical Society, ISBN 978-0-8218-1017-0...

Hypercomplex analysis Vector calculus List of complex analysis topics Monodromy theorem Riemann–Roch theorem Runge's theorem "Industrial Applications...

ISBN 9781420035223. Daniel Frohardt and Kay Magaard, Composition Factors of Monodromy Groups, Annals of Mathematics Second Series, Vol. 154, No. 2 (Sep., 2001)...

defined by a Laurent polynomial. They introduced the zeta function of monodromy at ∞ and showed that, in the non-degenerate case, it closely agreed with...

n}} . These are the necessary and sufficient conditions for the based monodromy representation of the fundamental group π 1 ( P 1 ∖ { α i } i = 1 , …...

knot complement, let g : S → S {\displaystyle g:S\to S} represent the monodromy, then Δ K ( t ) = D e t ( t I − g ∗ ) {\displaystyle \Delta _{K}(t)={\rm...

S2CID 250830242. Child, M. S.; Weston, T.; Tennyson, J. (1999). "Quantum monodromy in the spectrum of H2O and other systems: New insight into the level structure...

Surfaces, 1997 (joint author) Random Matrices, Frobenius Eigenvalues and Monodromy, 1998 Peter Sarnak (2000). "Some problems in Number Theory, Analysis and...

Lisovyy, O.; Tykhyy, Yu. (2013). "Painlevé VI connection problem and monodromy of c = 1 conformal blocks". Journal of High Energy Physics. 2013 (12):...