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New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-novikov Theory (Hardcover)
Loot Price: R2,133
Discovery Miles 21 330
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New Topological Invariants For Real- And Angle-valued Maps: An Alternative To Morse-novikov Theory (Hardcover)
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Total price: R2,153
Discovery Miles: 21 530
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This book is about new topological invariants of real- and
angle-valued maps inspired by Morse-Novikov theory, a chapter of
topology, which has recently raised interest outside of
mathematics; for example, in data analysis, shape recognition,
computer science and physics. They are the backbone of what the
author proposes as a computational alternative to Morse-Novikov
theory, referred to in this book as AMN-theory.These invariants are
on one side analogues of rest points, instantons and closed
trajectories of vector fields and on the other side, refine basic
topological invariants like homology and monodromy. They are
associated to tame maps, considerably more general than Morse maps,
that are defined on spaces which are considerably more general than
manifolds. They are computable by computer implementable algorithms
and have strong robustness properties. They relate the dynamics of
flows that admit the map as 'Lyapunov map' to the topology of the
underlying space, in a similar manner as Morse-Novikov theory does.
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