Differential Galois Theory and Integration (Q5022175)

scientific article; zbMATH DE number 7458366

Language	Label	Description	Also known as
English	Differential Galois Theory and Integration	scientific article; zbMATH DE number 7458366

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instance of

scholarly article

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title

Differential Galois Theory and Integration (English)

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zbMATH Open document ID

1489.12019

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DOI

10.1007/978-3-030-80219-6_7

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Texts & Monographs in Symbolic Computation

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publication date

18 January 2022

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full work available at URL

https://arxiv.org/abs/2104.09786

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Mathematics Subject Classification ID

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Lie-Galois algebra

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reducible differential equation

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reduced differential equation

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describes a project that uses

Maple

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MaRDI profile type

MaRDI publication profile

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A differential Galois approach to path integrals

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A reduced form for linear differential systems and its application to integrability of Hamiltonian systems

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The Importance of the Ising Model

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Q3324796

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Unipotent radicals of differential Galois group and integrals of solutions of inhomogeneous equations

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Calculating the Galois group of $L_1(L_2(y))=0,$ $L_1, L_2$ completely reducible operators

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Galoisian methods for testing irreducibility of order two nonlinear differential equations

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Q4790565

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Picard-Vessiot Extensions of Real Differential Fields

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Q3596942

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A characterization of reduced forms of linear differential systems

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Solvable-by-finite groups as differential Galois groups

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Liouville integrability: an effective Morales-Ramis-Simó theorem

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Reduced forms of linear differential systems and the intrinsic Galois-Lie algebra of Katz

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Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System

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An algorithm for solving second order linear homogeneous differential equations

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Note on Kovacic's algorithm

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Solving second order linear differential equations with Klein's theorem

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Integration of solutions of linear functional equations

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Q4226958

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Advanced Statistical Mechanics

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The saga of the Ising susceptibility

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Fuchs versus Painlevé

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Globally nilpotent differential operators and the square Ising model

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Renormalization, isogenies, and rational symmetries of differential equations

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The Ising model: from elliptic curves to modular forms and Calabi–Yau equations

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Differential algebra on lattice Green functions and Calabi–Yau operators

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Canonical decomposition of irreducible linear differential operators with symplectic or orthogonal differential Galois groups

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Lattice Green functions: the<i>d</i>-dimensional face-centered cubic lattice,<i>d</i>= 8, 9, 10, 11, 12

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Lattice Green functions of the higher-dimensional face-centered cubic lattices

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Diagonals of rational functions, pullbacked $\boldsymbol{_2F_1}$ hypergeometric functions and modular forms

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Maximally reducible monodromy of bivariate hypergeometric systems

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Differential reduction of generalized hypergeometric functions from Feynman diagrams: one-variable case

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Counting the number of master integrals for sunrise diagrams via the Mellin-Barnes representation

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Analytic tools for Feynman integrals

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Solving differential equations for Feynman integrals by expansions near singular points

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Iterated binomial sums and their associated iterated integrals

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Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I

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Effective algorithm of analysis of integrability via the Ziglin's method

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Galoisian obstructions to integrability of Hamiltonian systems. II.

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Integrability of Hamiltonian systems and differential Galois groups of higher variational equations

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Galoisian obstructions to non-Hamiltonian integrability

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The meromorphic non-integrability of the three-body problem

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Q4459882

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On the meromorphic non-integrability of some $N$-body problems

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Non-integrability of the equal mass $n$-body problem with non-zero angular momentum

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Algebraic proof of the non-integrability of Hill's problem

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Swinging Atwood Machine: experimental and numerical results, and a theoretical study

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Finding Integral Linear Dependencies of Algebraic Numbers and Algebraic Lie Algebras

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On the exponential solution of differential equations for a linear operator

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Lie Algebraic Solution of Linear Differential Equations

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On Global Representations of the Solutions of Linear Differential Equations as a Product of Exponentials

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Differential Galois Theory of Algebraic Lie-Vessiot Systems

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A Reduction Method for Higher Order Variational Equations of Hamiltonian Systems

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Liouvillian solutions of linear differential equations with Liouvillian coefficients

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On rational solutions of systems of linear differential equations

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On the Determination of Ziglin Monodromy Groups

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