Ebook: The Geometry of Higher-Order Hamilton Spaces: Applications to Hamiltonian Mechanics

From the reviews:

"The book is devoted to an extensive study of formal-geometric properties of higher-order nondegenerate one-dimensional variational integrals. … The author’s approach is useful for the construction of geometric models … . The book is precisely written, very clear, in principle self-contained and can be understood by non-specialists." (Jan Chrastina, Zentralblatt MATH, Vol. 1044 (19), 2004)

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Content:
Front Matter....Pages i-xvi
Geometry of the k-Tangent Bundle T k M ....Pages 1-26
Lagrange Spaces of Higher Order....Pages 27-42
Finsler Spaces of Order k ....Pages 43-57
The Geometry of the Dual of k-Tangent Bundle....Pages 59-75
The Variational Problem for the Hamiltonians of Order k ....Pages 77-95
Dual Semispray. Nonlinear Connections....Pages 97-123
Linear Connections on the Manifold T* k M....Pages 125-149
Hamilton Spaces of Order k ? 1....Pages 151-176
Subspaces in Hamilton Spaces of Order k ....Pages 177-197
The Cartan Spaces of Order k as Dual of Finsler Spaces of Order k ....Pages 199-220
Generalized Hamilton and Cartan Spaces of Order k. Applications to Hamiltonian Relativistic Optics....Pages 221-234
Back Matter....Pages 235-247

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Content:
Front Matter....Pages i-xvi
Geometry of the k-Tangent Bundle T k M ....Pages 1-26
Lagrange Spaces of Higher Order....Pages 27-42
Finsler Spaces of Order k ....Pages 43-57
The Geometry of the Dual of k-Tangent Bundle....Pages 59-75
The Variational Problem for the Hamiltonians of Order k ....Pages 77-95
Dual Semispray. Nonlinear Connections....Pages 97-123
Linear Connections on the Manifold T* k M....Pages 125-149
Hamilton Spaces of Order k ? 1....Pages 151-176
Subspaces in Hamilton Spaces of Order k ....Pages 177-197
The Cartan Spaces of Order k as Dual of Finsler Spaces of Order k ....Pages 199-220
Generalized Hamilton and Cartan Spaces of Order k. Applications to Hamiltonian Relativistic Optics....Pages 221-234
Back Matter....Pages 235-247
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