Linear connections for systems of higher order differential equations

• Autores: Ioan Bucataru
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 2, 2005, págs. 315-332
• Idioma: inglés
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• Resumen

  • For a system of (k+1) order differential equations (or a semispray of order k on the tangent bundle of order k) we determine a nonlinear connection induced by it. This nonlinear connection induces a linear connection D on the total space of the tangent bundle of order k, that is called the Berwald connection. Using the Cartan's structure equations of the Berwald connection, we determine the conditions by which a system of (k+1) order differential equations is linearizable with respect to the accelerations of order k. This is a generalization for the k=1 case presented in the first part of the paper.