Structural Complexity and Dynamical Systems

  • Renzo L. RiccaEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 1973)


With this paper we want to pay tribute to 150 years of work on topological fluid mechanics. For this, we review Helmholtz's (1858) original contribution on topological issues related to vortex motion. Some recent results on aspects of structural complexity analysis of fluid flows are presented and discussed, as well as new results on topological bounds on the energy of magnetic knots and links in ideal magnetohydrodynamics, and on helicity-crossing number relations in dissipative fluids.


Double Point Vortex Line Vortex Motion Magnetic Helicity Reidemeister Move 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Mathematics and ApplicationsUniversity of Milano-BicoccaMilanoITALY

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