%0 Journal Article %1 Froehlich_2012 %A Froehlich, Stefan %A Cvitanović, Predrag %D 2012 %J Communications in Nonlinear Science and Numerical Simulation %K fluid-dynamics nonlinearity turbulence %N 5 %P 2074 - 2084 %R 10.1016/j.cnsns.2011.07.007 %T Reduction of continuous symmetries of chaotic flows by the method of slices %U http://www.sciencedirect.com/science/article/pii/S1007570411003753 %V 17 %X We study continuous symmetry reduction of dynamical systems by the method of slices (method of moving frames) and show that a ‘slice’ defined by minimizing the distance to a single generic ‘template’ intersects the group orbit of every point in the full state space. Global symmetry reduction by a single slice is, however, not natural for a chaotic/ turbulent flow; it is better to cover the reduced state space by a set of slices, one for each dynamically prominent unstable pattern. Judiciously chosen, such tessellation eliminates the singular traversals of the inflection hyperplane that comes along with each slice, an artifact of using the templates local group linearization globally. We compute the jump in the reduced state space induced by crossing the inflection hyperplane. As an illustration of the method, we reduce the SO (2) symmetry of the complex Lorenz equations.

@article{Froehlich_2012, abstract = {We study continuous symmetry reduction of dynamical systems by the method of slices (method of moving frames) and show that a ‘slice’ defined by minimizing the distance to a single generic ‘template’ intersects the group orbit of every point in the full state space. Global symmetry reduction by a single slice is, however, not natural for a chaotic/ turbulent flow; it is better to cover the reduced state space by a set of slices, one for each dynamically prominent unstable pattern. Judiciously chosen, such tessellation eliminates the singular traversals of the inflection hyperplane that comes along with each slice, an artifact of using the templates local group linearization globally. We compute the jump in the reduced state space induced by crossing the inflection hyperplane. As an illustration of the method, we reduce the SO (2) symmetry of the complex Lorenz equations.}, added-at = {2013-02-14T23:42:11.000+0100}, author = {Froehlich, Stefan and Cvitanović, Predrag}, biburl = {https://www.bibsonomy.org/bibtex/25bf958ee10a01bdfd9badd7be5577e97/knielson}, description = {ScienceDirect.com - Communications in Nonlinear Science and Numerical Simulation - Reduction of continuous symmetries of chaotic flows by the method of slices}, doi = {10.1016/j.cnsns.2011.07.007}, interhash = {588f72d64eec11bc1c1967f47c3cf663}, intrahash = {5bf958ee10a01bdfd9badd7be5577e97}, issn = {1007-5704}, journal = {Communications in Nonlinear Science and Numerical Simulation}, keywords = {fluid-dynamics nonlinearity turbulence}, note = {Special Issue: Mathematical Structure of Fluids and Plasmas <ce:subtitle>Dedicated to the 60th birthday of Phil Morrison</ce:subtitle>}, number = 5, pages = {2074 - 2084}, timestamp = {2013-02-14T23:42:11.000+0100}, title = {Reduction of continuous symmetries of chaotic flows by the method of slices}, url = {http://www.sciencedirect.com/science/article/pii/S1007570411003753}, volume = 17, year = 2012 }