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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CANE

Book 1999d as generalizations of classical non-integrability results by Poincaré and Lyapunov, as well as more recent results by Ziglin and Yoshida. Thus, by means of the differential Galois theory it is not only possible to understand all these approaches in a unified way but also to improve them. Several i

Trigger-Point

Differential Galois Theory,ility” 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

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盡忠

Three Models,the Sitnikov system in celestial mechanics. We note that, from the differential Galois theory of Chapter 2 (we shall need only the theorem of Kimura and the algorithm of Kovacic) and from our results of Chapter 4, the methods proposed here are completely systematic and elementary. In our opinion, th

colony

,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 Chapt

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A Connection with Chaotic Dynamics,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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魔鬼在游行

Maria Luisa De Rimini,Giovanni Borrelligrability is well defined for these systems, it is very important to clarify what kind of regularity is allowed for the first integrals: differentiability or analyticity in the real situation, analytic, meromorphic or algebraic (meromorphic and meromorphic at infinity) first integrals in the complex setting.

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