Titlebook: Differential Galois Theory and Non-Integrability of Hamiltonian Systems; Juan J. Morales Ruiz Book 1999 Springer Basel 1999 Dynamical Syst

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極大痛苦

,An Application of the Lamé Equation,n and A and . are, in general, complex parameters. It is assumed, in what follows, that the roots of the polynomial . associated to . are simple (otherwise . is reduced to elementary functions). This is ensured if the discriminant.is non-zero, where g. and g. are the associated invariants (see Chapter 2).

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Analogy

https://doi.org/10.1007/978-3-0348-8718-2Dynamical System; Galois group; Galois theory; algebra; differential algebra; differential equation; dynam

和藹

https://doi.org/10.1007/978-3-031-54196-4ility” i.e., solutions in closed form: an equation is integrable if the general solution is obtained by a combination of algebraic functions (over the coefficient field), exponentiation of quadratures and quadratures. Furthermore, all information about the integrability of the equation is coded in t

卡死偷電

Maria Luisa De Rimini,Giovanni Borrelliy i.e., Liouville integrability: the existence of . independent first integrals in involution, . being the number of degrees of freedom. Although integrability is well defined for these systems, it is very important to clarify what kind of regularity is allowed for the first integrals: differentiabi

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Humble

The Bone Pathway: 223Ra-Dichloride,c differential Galois criterion of non-integrability based on the analysis in the . phase space of the variational equations along a particular integral curve. This problem was proposed in Section 6.4 (Question 2).

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Differential Galois Theory and Non-Integrability of Hamiltonian Systems