Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems
A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families...
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| Published in | Physics letters. A Vol. 375; no. 19; pp. 1972 - 1975 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
09.05.2011
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| Abstract | A new
n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures.
► A new family of Poisson structures is globally characterized and analyzed. ► Such family is globally defined for arbitrary values of the dimension and the rank. ► Global construction of Casimir invariants and Darboux canonical form is provided. ► Very diverse and previously known solutions of physical interest are generalized. |
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| AbstractList | A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given that include the generalization of previously known solution families such as the separable Poisson structures. ► A new family of Poisson structures is globally characterized and analyzed. ► Such family is globally defined for arbitrary values of the dimension and the rank. ► Global construction of Casimir invariants and Darboux canonical form is provided. ► Very diverse and previously known solutions of physical interest are generalized. |
| Author | Hernández-Bermejo, Benito |
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| References | Castagnino, Gadella, Lara (br0050) 2006; 30 García, Hernández-Bermejo (br0100) 2010; 239 Hernández-Bermejo (br0230) 2006; 355 Blaszak, Gürses, Zheltukhin (br0030) 2009; 42 Nutku (br0160) 1990; 23 Byrnes, Haggar, Quispel (br0170) 1999; 272 Gürses, Guseinov, Zheltukhin (br0040) 2009; 50 Damianou (br0070) 2004; 17 Damianou, Sophocleous (br0080) 2005; 18 Abadoğlu, Gūmral (br0120) 2009; 238 Hernández-Bermejo (br0150) 2001; 42 Damianou, Kouzaris (br0060) 2003; 36 Gūmral, Nutku (br0110) 1993; 34 Hernández-Bermejo (br0240) 2007; 48 Hernández-Bermejo (br0190) 2008; 344 Hernández-Bermejo, Fairén (br0210) 2000; 271 Hernández-Bermejo (br0200) 2010; 374 Hernández-Bermejo (br0260) 2009; 22 Hernández-Bermejo (br0250) 2008; 372 Tudoran, Gîrban (br0130) 2010; 11 Hernández-Bermejo, Fairén (br0140) 1998; 39 Ayres (br0270) 1962 Perlick (br0180) 1992; 33 Ay, Gürses, Zheltukhin (br0020) 2003; 44 Olver (br0010) 1993 David, Holm (br0090) 1992; 2 Hernández-Bermejo (br0220) 2006; 47 Damianou (10.1016/j.physleta.2011.03.053_br0070) 2004; 17 Castagnino (10.1016/j.physleta.2011.03.053_br0050) 2006; 30 Byrnes (10.1016/j.physleta.2011.03.053_br0170) 1999; 272 Gūmral (10.1016/j.physleta.2011.03.053_br0110) 1993; 34 Gürses (10.1016/j.physleta.2011.03.053_br0040) 2009; 50 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0190) 2008; 344 Perlick (10.1016/j.physleta.2011.03.053_br0180) 1992; 33 Blaszak (10.1016/j.physleta.2011.03.053_br0030) 2009; 42 García (10.1016/j.physleta.2011.03.053_br0100) 2010; 239 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0210) 2000; 271 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0230) 2006; 355 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0220) 2006; 47 David (10.1016/j.physleta.2011.03.053_br0090) 1992; 2 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0260) 2009; 22 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0240) 2007; 48 Ay (10.1016/j.physleta.2011.03.053_br0020) 2003; 44 Tudoran (10.1016/j.physleta.2011.03.053_br0130) 2010; 11 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0140) 1998; 39 Damianou (10.1016/j.physleta.2011.03.053_br0060) 2003; 36 Nutku (10.1016/j.physleta.2011.03.053_br0160) 1990; 23 Damianou (10.1016/j.physleta.2011.03.053_br0080) 2005; 18 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0250) 2008; 372 Olver (10.1016/j.physleta.2011.03.053_br0010) 1993 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0200) 2010; 374 Hernández-Bermejo (10.1016/j.physleta.2011.03.053_br0150) 2001; 42 Abadoğlu (10.1016/j.physleta.2011.03.053_br0120) 2009; 238 Ayres (10.1016/j.physleta.2011.03.053_br0270) 1962 |
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n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic... A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic... |
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| SubjectTerms | Atomic structure Canonical forms Casimir invariants Construction Darboux canonical form Finite-dimensional Poisson systems Hamiltonian systems Jacobi identities Reduction Separation Solid state physics |
| Title | Generalization of the separation of variables in the Jacobi identities for finite-dimensional Poisson systems |
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