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2015, 2015(special): 213-222. doi: 10.3934/proc.2015.0213

Jacobi fields for second-order differential equations on Lie algebroids

José F. Cariñena 1, , Irina Gheorghiu 2, and  Eduardo Martínez 3,

1. 

IUMA and Department of Theoretical Physics, University of Zaragoza, Spain
2. 

Department of Theoretical Physics, University of Zaragoza
3. 

IUMA and Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza

Received  September 2014 Revised  January 2015 Published  November 2015

We generalize the concept of Jacobi field for general second-order differential equations on a manifold and on a Lie algebroid. The Jacobi equation is expressed in terms of the dynamical covariant derivative and the generalized Jacobi endomorphism associated to the given differential equation.
Keywords: second-order di erential equations, Jacobi fi elds, Jacobi equation., Lie algebroids.
Mathematics Subject Classification: 34A26, 58Z05, 58Cx.
Citation: José F. Cariñena, Irina Gheorghiu, Eduardo Martínez. Jacobi fields for second-order differential equations on Lie algebroids. Conference Publications, 2015, 2015 (special) : 213-222. doi: 10.3934/proc.2015.0213
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show all references

References:
[1]

In Group Theoretical Methods in Physics II (Moscow 1990), Nova Science Publishers, New York, 1991 Google Scholar

[2]

Discrete and Continuous Dynamical Systems A, 24 2 (2009), 213-271 doi: 10.3934/dcds.2009.24.213.  Google Scholar

[3]

Cambridge University Press, 1986  Google Scholar

[4]

J. Phys. A: Math. Gen., 38 (2005), R241-R308  Google Scholar

[5]

Ann. Inst. H. Poincaré Phys. Théor., 45 (1986), 1, 1-28  Google Scholar

[6]

Unpublished (1997) Google Scholar

[7]

Cambridge University Press, 2005  Google Scholar

[8]

Acta Appl. Math., 67 (2001), 295-320  Google Scholar

[9]

Reports on Mathematical Physics 53 (2004), 79-90 doi: 10.1016/S0034-4877(04)90005-5.  Google Scholar

[10]

J. Phys. A: Math. Gen., 38 (2005), 7145-7160 doi: 10.1088/0305-4470/38/32/005.  Google Scholar

[11]

ESAIM: Control, Optimisation and Calculus of Variations 14 02, 2007, 356-380 doi: 10.1051/cocv:2007056.  Google Scholar

[12]

Differential Geometry and its Applications 3 (1993) 1-29  Google Scholar

[13]

Rend. Sem. Mat. Univ. Politec. Torino 54 (1996), 365-372  Google Scholar

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