Now Australia's Biggest Toy Shop

Shop over 1.5 Million Toys in our Huge New Range

The Geometry of Higher-order Hamilton Spaces

Product Details

Promotional Information

Springer Book Archives

Table of Contents

1 Geometry of the k-Tangent Bundle TkM.- 1.1 The Category of k-Accelerations Bundles.- 1.2 Liouville Vector Fields. k-Semisprays.- 1.3 Nonlinear Connections.- 1.4 The Dual Coefficients of a Nonlinear Connection.- 1.5 The Determination of a Nonlinear Connection.- 1.6 d-Tensor Fields. N-Linear Connections.- 1.7 Torsion and Curvature.- 2 Lagrange Spaces of Higher Order.- 2.1 Lagrangians of Order k.- 2.2 Variational Problem.- 2.3 Higher Order Energies.- 2.4 Jacobi-Ostrogradski Momenta.- 2.5 Higher Order Lagrange Spaces.- 2.6 Canonical Metrical N-Connections.- 2.7 Generalized Lagrange Spaces of Order k.- 3 Finsler Spaces of Order k.- 3.1 Spaces F(k)n.- 3.2 Cartan Nonlinear Connection in F(k)n.- 3.3 The Cartan Metrical N-Linear Connection.- 4 The Geometry of the Dual of k-Tangent Bundle.- 4.1 The Dual Bundle (T*k M, ?*k, M).- 4.2 Vertical Distributions. Liouville Vector Fields.- 4.3 The Structures J and J*.- 4.4 Canonical Poisson Structures on T*kM.- 4.5 Homogeneity.- 5 The Variational Problem for the Hamiltonians of Order k.- 5.1 The Hamilton-Jacobi Equations.- 5.2 Zermelo Conditions.- 5.3 Higher Order Energies. Conservation of Energy ?k ?1(H).- 5.4 The Jacobi-Ostrogradski Momenta.- 5.5 Noether Type Theorems.- 6 Dual Semispray. Nonlinear Connections.- 6.1 Dual Semispray.- 6.2 Nonlinear Connections.- 6.3 The Dual Coefficients of the Nonlinear Connection N.- 6.4 The Determination of the Nonlinear Connection by a Dual k-Semispray.- 6.5 Lie Brackets. Exterior Differential.- 6.6 The Almost Product Structure ?. The Almost Contact Structure $$ mathbb{F} $$.- 6.7 The Riemannian Structure G on T*kM.- 6.8 The Riemannian Almost Contact Structure $$(mathop mathbb{G}limits^ vee ,mathop mathbb{F}limits^ vee )$$.- 7 Linear Connections on the Manifold T*kM.- 7.1 The Algebra of Distinguished Tensor Fields.- 7.2 N-Linear Connections.- 7.3 The Torsion and Curvature of an N-Linear Connection.- 7.4 The Coefficients of a N-Linear Connection.- 7.5 The h-,??- and ?k-Covariant Derivatives in Local Adapted Basis.- 7.6 Ricci Identities. Local Expressions of d-Tensor of Curvature and Torsion. Bianchi Identities.- 7.7 Parallelism of the Vector Fields on the Manifold T*kM.- 7.8 Structure Equations of a N-Linear Connection.- 8 Hamilton Spaces of Order k ? 1.- 8.1 The Spaces H(k)n.- 8.2 The k-Tangent Structure J and the Adjoint k-Tangent Structure J*.- 8.3 The Canonical Poisson Structure of the Hamilton Space H(k)n.- 8.4 Legendre Mapping Determined by a Lagrange Space L(k)n= (M, L).- 8.5 Legendre Mapping Determined by a Hamilton Space of Order k.- 8.6 The Canonical Nonlinear Connection of the Space H(k)n.- 8.7 Canonical Metrical N-Linear Connection of the Space H(k)n.- 8.8 The Hamilton Space H(k)n of Electrodynamics.- 8.9 The Riemannian Almost Contact Structure Determined by the Hamilton Space H(k)n.- 9 Subspaces in Hamilton Spaces of Order k.- 9.1 Submanifolds $${T^{*k}}mathop Mlimits^ vee$$ in the Manifold T*kM.- 9.2 Hamilton Subspaces $${{mathop Hlimits^ vee} ^{(k)m}}$$ in H(k)n. Darboux Frames.- 9.3 Induced Nonlinear Connection.- 9.4 The Relative Covariant Derivative.- 9.5 The Gauss-Weingarten Formula.- 9.6 The Gauss-Codazzi Equations.- 10 The Cartan Spaces of Order k as Dual of Finsler Spaces of Order k.- 10.1 C(k)n-Spaces.- 10.2 Geometrical Properties of the Cartan Spaces of Order k.- 10.3 Canonical Presymplectic Structures, Variational Problem of the Space C(kn).- 10.4 The Cartan Spaces C(k)n as Dual of Finsler Spaces F(k)n.- 10.5 Canonical Nonlinear Connection. N-Linear Connections.- 10.6 Parallelism of Vector Fields in Cartan Space C(kn).- 10.7 Structure Equations of Metrical Canonical N-Connection.- 10.8 Riemannian Almost Contact Structure of the Space C(kn).- 11 Generalized Hamilton and Cartan Spaces of Order k. Applications to Hamiltonian Relativistic Optics.- 11.1 The Space GH(kn).- 11.2 Metrical N-Linear Connections.- 11.3 Hamiltonian Relativistic Optics.- 11.4 The Metrical Almost Contact Structure of the Space GH(kn).- 11.5 Generalized Cartan Space of Order k.- References.


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)

Ask a Question About this Product More...
Write your question below:
Look for similar items by category
Home » Books » Science » Mathematics » Applied
How Fishpond Works
Fishpond works with suppliers all over the world to bring you a huge selection of products, really great prices, and delivery included on over 25 million products that we sell. We do our best every day to make Fishpond an awesome place for customers to shop and get what they want — all at the best prices online.
Webmasters, Bloggers & Website Owners
You can earn a 5% commission by selling The Geometry of Higher-order Hamilton Spaces: Applications to Hamiltonian Mechanics (Fundamental Theories of Physics) on your website. It's easy to get started - we will give you example code. After you're set-up, your website can earn you money while you work, play or even sleep! You should start right now!
Authors / Publishers
Are you the Author or Publisher of a book? Or the manufacturer of one of the millions of products that we sell. You can improve sales and grow your revenue by submitting additional information on this title. The better the information we have about a product, the more we will sell!
Back to top