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An Introduction to the Geometry and Topology of Fluid Flows

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Cover of 'An Introduction to the Geometry and Topology of Fluid Flows'

Table of Contents

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    Book Overview
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    Chapter 1 Some Remarks on Topological Fluid Mechanics
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    Chapter 2 Differential Geometry of Curves and Surfaces
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    Chapter 3 Topology in Four Days
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    Chapter 4 Elements of Classical Knot Theory
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    Chapter 5 An Introduction to Knot Theory
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    Chapter 6 Fluid Mechanics and Mathematical Structures
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    Chapter 7 Introduction to a Geometrical Theory of Fluid Flows and Dynamical Systems
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    Chapter 8 Streamline Patterns and Their Bifurcations Using Methods from Dynamical Systems
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    Chapter 9 Topological Features Of Inviscid Flows
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    Chapter 10 Geometric and Topological Aspects of Vortex Motion
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    Chapter 11 Topology Bounds the Energy
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    Chapter 12 Measures of Topological Structure in Magnetic Fields
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    Chapter 13 Diffeomorphisms, Braids and Flows
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    Chapter 14 Variational Principles, Geometry and Topology of Lagrangian-Averaged Fluid Dynamics
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    Chapter 15 The Geometry of Reconnection
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    Chapter 16 Euler Singularities from the Lagrangian Viewpoint
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    Chapter 17 Analysis of a Candidate Flow For Hydrodynamic Blowup
Attention for Chapter 7: Introduction to a Geometrical Theory of Fluid Flows and Dynamical Systems
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