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The Helmholtz decomposition splits a sufficiently smooth vector field into a gradient field and a divergence-free rotation field.
“Über die Zerlegung unendlicher Vektorfelder”
Otto Blumenthal · 1905
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“L’intégrale de Riemann-Liouville et le problème de Cauchy”
Marcel Riesz · 1949
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“Deterministic Nonperiodic Flow”
Edward. Lorenz · 1963
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Otto. Rössler · 1976
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“Lotka-Volterra Population Models”
Peter. Wangersky · 1978
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“A Mathematical Introduction to Fluid Mechanics”, Texts in Applied Mathematics 4
Alexandre. Chorin and Jerrold. Marsden · 1990
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“Strange Attractors: The Locus of Chaos”
Heinz-Otto Peitgen, Hartmut Jürgens and Dietmar Saupe · 1992
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“Introduction to Complex Analysis Part II. Functions of Several Variables” 110
Boris Shabat · 1992
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“On Helmholtz’s Decomposition Theorem and Poissons’s Equation with an Infinite Domain”
Ton Tran-Cong · 1993
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“Balancing Survival and Extinction in Nonautonomous Competitive Lotka-Volterra Systems”
Francisco Montes and Mary Zeeman · 1995
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“Hodge Decomposition—A Method for Solving Boundary Value Problems” 1607
Günter Schwarz · 1995
Cited alongside, same era.
“Uniqueness and reconstruction for the anisotropic Helmholtz decomposition”
George Dassios and Ismo. Lindell · 2002
Cited alongside, same era.
“A Concise Handbook of Mathematics, Physics, and Engineering Sciences”
Andrei. Polyanin and Alexei Chernoutsan · 2010
Cited alongside, same era.
“The Helmholtz-Hodge Decomposition—A Survey”
Harsh Bhatia, Gregory Norgard, Valerio Pascucci and Peer-Timo Bremer · 2012
“Quasi-potential landscape in complex multi-stable systems”
Joseph Zhou, M… Aliyu, Erik Aurell and Sui Huang · 2012
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“The Helmholtz decomposition revisited”
Dietmar Petrascheck · 2015
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“On the Helmholtz Theorem and Its Generalization for Multi-Layers”
Alp Kustepeli · 2016
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“A Constructive Proof of Helmholtz’s Theorem”
Bernardo De and José. Sabina · 2019
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“Construction of Lyapunov functions using Helmholtz–Hodge decomposition”
Tomoharu Suda · 2019
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“Second Order Linear Differential Operators over High Rank Tensor Fields”
D.. Georgievskii · 2020
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Cited alongside, same era.
“Helmholtz Decomposition and Rotation Potentials in n-dimensional Cartesian Coordinates”, 2021
Erhard Glötzl and Oliver Richters · 2012
Cited alongside, same era.
“Trente-Cinquième Leçon”
Augustin-Louis Cauchy
Cited in the paper.
“Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen”
Hermann von Helmholtz
Cited in the paper.
“On the Dynamical Theory of Diffraction”
George Stokes
Cited in the paper.
“Helmholtz decomposition and potential functions for n-dimensional analytic vector fields”
Erhard Glötzl and Oliver Richters · 2023
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