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Morse Theory Of Gradient Flows, Concavity And Complexity On Manifolds With Boundary (Hardcover)
Loot Price: R5,199
Discovery Miles 51 990
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Morse Theory Of Gradient Flows, Concavity And Complexity On Manifolds With Boundary (Hardcover)
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Total price: R5,219
Discovery Miles: 52 190
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This monograph is an account of the author's investigations of
gradient vector flows on compact manifolds with boundary. Many
mathematical structures and constructions in the book fit
comfortably in the framework of Morse Theory and, more generally,
of the Singularity Theory of smooth maps.The geometric and
combinatorial structures, arising from the interactions of vector
flows with the boundary of the manifold, are surprisingly rich.
This geometric setting leads organically to many encounters with
Singularity Theory, Combinatorics, Differential Topology,
Differential Geometry, Dynamical Systems, and especially with the
boundary value problems for ordinary differential equations. This
diversity of connections animates the book and is the main
motivation behind it.The book is divided into two parts. The first
part describes the flows in three dimensions. It is more pictorial
in nature. The second part deals with the multi-dimensional flows,
and thus is more analytical. Each of the nine chapters starts with
a description of its purpose and main results. This organization
provides the reader with independent entrances into different
chapters.
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