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A discrete hierarchy of double bracket equations and a class of negative power series
| 1. | Instituto de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia, Calle 67 No. 53 -108, Medellin, Colombia |
| 2. | Departamento de Ciencias Básicas, Universidad del Sinú, Cra 1w No. 38-153, Barrio Juan XXⅢ, Montería, Colombia |
The space of negative power series of $z$ on $\{z\in \mathbb{C}:|z|>1\}$ can also be parametrized by means of a system of double bracket differential equations. To show this parametrization we introduce a group factorization for equation system. This work, for the case of a double bracket system, is a continuation of an earlier study discussed in The discrete KP hierarchy and the negative power series on the complex plane. Comp. and App. Math. 32 (2013), 483-493 for the case of one bracket system.
References:
| [1] |
L. Benitez-Babilonia, R. Felipe and N. López Reyes,
Algebraic analysis of a discrete hierarchy of double bracket equations, Diff. Equ. and Dyn. Syst., 17 (2009), 77-90.
doi: 10.1007/s12591-009-0006-x. |
| [2] |
A. Bensoussan, G. Da Prato, M. C. Delfour and S. K. Mitter, Representation and Control of Infinite Dimensional Systems: Foundations and Applications, Birkhäuser, Boston, 2007.
doi: 10.1007/978-0-8176-4581-6. |
| [3] |
R. F. Curtain and H. J. Zwart, An Introduction to Infinite Dimensional Systems Theory, Texts in Applied Mathematics 21, Springer-Verlag, New York, 1995.
doi: 978-1-4612-8702-5. |
| [4] |
R. Felipe,
Algebraic aspects of Brockett type equations, Physica D, 132 (1999), 287-297.
doi: 10.1016/S0167-2789(99)00025-1. |
| [5] |
R. Felipe and F. Ongay,
Algebraic aspects of the discrete KP hierarchy, Linear Alg. and its Appl., 338 (2001), 1-17.
doi: 10.1016/S0024-3795(01)00365-2. |
| [6] |
R. Felipe and N. López Reyes, The finite discrete KP hierarchy and the rational functions Disc. Dyna. in Natu. and Soci., 2008 (2008), Article ID 792632, 10pp.
doi: 10.1155/2008/792632. |
| [7] |
R. Felipe and N. López Reyes,
Integrability of a double bracket system, Rev. Integración, 31 (2013), 15-23.
|
| [8] |
B. Jacob and H. J. Zwart,
Properties of the realization of inner functions, Math. Cont. Sign. Syst., 15 (2002), 356-379.
doi: 10.1016/S0167-6911(01)00113-X. |
| [9] |
N. López Reyes, R. Felipe and T. Castro Polo,
The discrete KP hierarchy and the negative power series on the complex plane, Comp. and Appl. Math., 32 (2013), 483-493.
doi: 10.1007/s40314-013-0031-9. |
| [10] |
Y. Nakamura,
Geometry of rational functions and nonlinear integrable systems, SIAM J. Math. Anal., 22 (1991), 1744-1754.
doi: 10.1137/0522108. |
| [11] |
T.-Y. Tam,
Gradiente flows and double bracket equations, Diff. Geom. Appl., 20 (2004), 209-224.
doi: 10.1016/j.difgeo.2003.10.008. |
| [12] |
H. J. Zwart,
Transfer functions for infinite-dimensional systems, Syst. Cont. Lett., 52 (2004), 247-255.
doi: 10.1016/j.sysconle.2004.02.002. |
show all references
References:
| [1] |
L. Benitez-Babilonia, R. Felipe and N. López Reyes,
Algebraic analysis of a discrete hierarchy of double bracket equations, Diff. Equ. and Dyn. Syst., 17 (2009), 77-90.
doi: 10.1007/s12591-009-0006-x. |
| [2] |
A. Bensoussan, G. Da Prato, M. C. Delfour and S. K. Mitter, Representation and Control of Infinite Dimensional Systems: Foundations and Applications, Birkhäuser, Boston, 2007.
doi: 10.1007/978-0-8176-4581-6. |
| [3] |
R. F. Curtain and H. J. Zwart, An Introduction to Infinite Dimensional Systems Theory, Texts in Applied Mathematics 21, Springer-Verlag, New York, 1995.
doi: 978-1-4612-8702-5. |
| [4] |
R. Felipe,
Algebraic aspects of Brockett type equations, Physica D, 132 (1999), 287-297.
doi: 10.1016/S0167-2789(99)00025-1. |
| [5] |
R. Felipe and F. Ongay,
Algebraic aspects of the discrete KP hierarchy, Linear Alg. and its Appl., 338 (2001), 1-17.
doi: 10.1016/S0024-3795(01)00365-2. |
| [6] |
R. Felipe and N. López Reyes, The finite discrete KP hierarchy and the rational functions Disc. Dyna. in Natu. and Soci., 2008 (2008), Article ID 792632, 10pp.
doi: 10.1155/2008/792632. |
| [7] |
R. Felipe and N. López Reyes,
Integrability of a double bracket system, Rev. Integración, 31 (2013), 15-23.
|
| [8] |
B. Jacob and H. J. Zwart,
Properties of the realization of inner functions, Math. Cont. Sign. Syst., 15 (2002), 356-379.
doi: 10.1016/S0167-6911(01)00113-X. |
| [9] |
N. López Reyes, R. Felipe and T. Castro Polo,
The discrete KP hierarchy and the negative power series on the complex plane, Comp. and Appl. Math., 32 (2013), 483-493.
doi: 10.1007/s40314-013-0031-9. |
| [10] |
Y. Nakamura,
Geometry of rational functions and nonlinear integrable systems, SIAM J. Math. Anal., 22 (1991), 1744-1754.
doi: 10.1137/0522108. |
| [11] |
T.-Y. Tam,
Gradiente flows and double bracket equations, Diff. Geom. Appl., 20 (2004), 209-224.
doi: 10.1016/j.difgeo.2003.10.008. |
| [12] |
H. J. Zwart,
Transfer functions for infinite-dimensional systems, Syst. Cont. Lett., 52 (2004), 247-255.
doi: 10.1016/j.sysconle.2004.02.002. |
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