By Krupka D., et al. (eds.)

This e-book is a set of survey articles in a vast box of the geometrical concept of the calculus of diversifications and its functions in research, geometry and physics. it's a commemorative quantity to have fun the sixty-fifth birthday of Professor Krupa, one of many founders of contemporary geometric variational concept, and an incredible contributor to this subject and its functions over the last thirty-five years. the entire authors invited to give a contribution to this quantity have tested excessive reputations of their box. The e-book will completely offer various vital effects, strategies and purposes which are frequently on hand merely through consulting unique papers in lots of assorted journals. it will likely be of curiosity to researchers in variational calculus, mathematical physics and the opposite similar parts of differential equations, common operators and geometric buildings. additionally, it's going to develop into a massive resource of present examine for doctoral scholars and postdoctorals in those fields.

**Read Online or Download Variations, geometry and physics, In honour of Demeter Krupka's 65 birthday PDF**

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**Sample text**

The formula for L was obtained in [74] and [75], and is called Tonti–Vainberg Lagrangian. Necessary and sufficient conditions for a dynamical form be locally variational were first studied by Helmholtz for the case of second order ordinary differential equations [30]. Lepage Forms in the Calculus of Variations 45 A generalisation to ordinary differential equations of an arbitrary order is due to Vanderbauwhede [76], and to higher-order partial differential equations to Anderson and Duchamp [3], and Krupka [40, 41].

Kol´aˇr and J. ) Masaryk University, Brno, 1996) 469– 478. [42] F. Takens, A global version of the inverse problem of calculus of variations, J. Diff. Geom. 14 (1979) 543–562. [43] W. M. Tulczyjew, The Euler-Lagrange resolution, In: Differential Geometric Methods in Mathematical Physics (Proc. Internat. , Aix-en-Provence, France, 1979, Lecture Notes in Math. 836, Springer, Berlin, 1980) 22–48. [44] A. M. Vinogradov, On the algebro-geometric foundations of Lagrangian field theory, Soviet. Math. Dokl.

102 (1980) 781–867. [4] A. V. Bocharov, V. N. Chetverikov, S. V. Duzhin, N. G. Khorkova, I. S. Krasilschik, A. V. Samokhin, Yu. N. Thorkov, A. M. Verbovetsky and A. M. Vinogradov, Symmetries and Conservation Laws for Differential Equations of Mathematical Physics ((I. S. Krasilschik and A. M. ) Amer. Math. , 1999). [5] L. Brink, P. di Vecchia and P. Howe, A locally supersymmetric and reparametrization invariant action for the spinning string, Phys. Lett. 65B(5) (1976) 471–474. [6] P. Dedecker, A property of differential forms in calculus of variations, Pac.