Leseprobe
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Global Variational Analysis
Marston Morse
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
This book builds upon the revolutionary discovery made in 1974 that when one passes from function f to a function J of paths joining two points A1≠A1 the connectivities R1 of the domain of f can be replaced by connectivities R1 over Q, common to the pathwise components of a basic Frechet space of classes of equivalent curves joining A1 to A1. The connectivities R1, termed "Frechet numbers," are proved independent of the choice of A1 ≠ A1, and of a replacement of Mn by any differential manifold homeomorphic to Mn.
Originally published in 1976.
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Kundenbewertungen
Inference, Intersection (set theory), Cramer's rule, Exotic sphere, Variable (mathematics), Topological space, Analytic function, Linear map, Axiom, Subset, Existential quantification, Invertible matrix, Partial derivative, Lagrange multiplier, Positive definiteness, N-sphere, Subsequence, Metric space, Without loss of generality, Weierstrass function, Countable set, First variation, Linear combination, Open set, Sturm separation theorem, Euler characteristic, Euler equations (fluid dynamics), Euler integral, Degeneracy (mathematics), Tuple, Einstein notation, Submanifold, Existence theorem, Continuous function, Curve, Deformation theory, Equation, Partial function, Differential structure, Phase space, Tensor algebra, Diffeomorphism, Compact space, Sign (mathematics), Differentiable manifold, Null vector, Homotopy, Maximal set, Rate of convergence, Resultant, Parametric equation, Taylor's theorem, Theorem, Riemannian manifold, Neighbourhood (mathematics), Topology, Jacobian matrix and determinant, Homeomorphism, Quadratic form, Boundary value problem, Derivative, Counting, Unit vector, Parameter, Pairwise, Special case, Euclidean space, Conjugate points, Cartesian coordinate system, Real variable