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Descripción
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| Bäcklund transformations (BTs) appear at the end of the XIXth century. They are introduced by the Swedish mathematician and physicist called Albert Victor Bäcklund as transformations of partial differential equations bringing solutions into solutions in a differential geometric context [Bäcklund 1874]. Independently, Darboux (1882) came to similar transformations in the context of second order ordinary differential equations. Since then, literature has provided BTs with specific properties such as preservation of the commuting Hamiltonians, canonicity, spectrality when there exists a dependence on a spectral parameter [Sasaki 1980, Zullo 2013]. In the nineties it was discovered how BTs appear in discretization of finite-dimensional integrable systems such as Euler top, Lagrange top, etc, [Suris 2003; Zullo 2013]. In this talk we focus on constructing Lie-Poisson integrators for complete integrable systems by using discrete variational principles [Marsden, West, 2001]. The systems under study are complete integrable because they admit a Lax pair representation whose conserved quantities are involutive, that is, mutually commuting. Here we search for geometric integrators that exactly preserve the integrability of the system. The results here extend the construction in [Suris, 2003] on matrix Lie groups to any finite-dimensional Lie group. The example of QR algorithm is provided on matrix Lie groups to recover intrinsically the discretizations considered by Suris (2003). | |
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Internacional
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Nombre congreso
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Congreso Bienal de la Real Sociedad Matemática Española. Sesión especial: "Avance en sistemas dinámicos y aplicaciones". |
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Tipo de participación
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730 |
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Lugar del congreso
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Zaragoza |
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DOI
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Fecha inicio congreso
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30/01/2017 |
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Fecha fin congreso
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03/02/2017 |
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