# American Institute of Mathematical Sciences

2003, 2003(Special): 68-77. doi: 10.3934/proc.2003.2003.68

## A reducible representation of the generalized symmetry group of a quasiperiodic flow

 1 Department of Mathematics, Brigham Young University, Provo, UT 84602

Received  June 2002 Published  April 2003

The generalized symmetry group of a quasiperiodic flow on a $n$-torus is the group theoretic normalizer, within the group of diffeomorphisms of the $n$-torus, of the one parameter abelian group of diffeomorphisms generated by the flow. Up to conjugacy, the generalized symmetry group of a quasiperiodic flow is determined by a system of uncoupled first order partial differential equations. New types of symmetries (other than the classical types of symmetries or time-reversing symmetries) may exist depending on certain algebraic relationships being satisfied by pair wise ratios of the frequencies of the quasiperiodic flow. These new symmetries, when they exist, are a dominant feature of a reducible linear representation of the generalized symmetry group in the de Rham cohomology of the $n$-torus.
Citation: L. Bakker. A reducible representation of the generalized symmetry group of a quasiperiodic flow. Conference Publications, 2003, 2003 (Special) : 68-77. doi: 10.3934/proc.2003.2003.68
 [1] Daniele Boffi, Franco Brezzi, Michel Fortin. Reduced symmetry elements in linear elasticity. Communications on Pure & Applied Analysis, 2009, 8 (1) : 95-121. doi: 10.3934/cpaa.2009.8.95 [2] Rui Qian, Rong Hu, Ya-Ping Fang. Local smooth representation of solution sets in parametric linear fractional programming problems. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 45-52. doi: 10.3934/naco.2019004 [3] Felix X.-F. Ye, Hong Qian. Stochastic dynamics Ⅱ: Finite random dynamical systems, linear representation, and entropy production. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4341-4366. doi: 10.3934/dcdsb.2019122 [4] Dmitry V. Zenkov. Linear conservation laws of nonholonomic systems with symmetry. Conference Publications, 2003, 2003 (Special) : 967-976. doi: 10.3934/proc.2003.2003.967 [5] Claudio Meneses. Linear phase space deformations with angular momentum symmetry. Journal of Geometric Mechanics, 2019, 11 (1) : 45-58. doi: 10.3934/jgm.2019003 [6] Pedro Freitas. The linear damped wave equation, Hamiltonian symmetry, and the importance of being odd. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 635-640. doi: 10.3934/dcds.1998.4.635 [7] Ángela Jiménez-Casas, Aníbal Rodríguez-Bernal. Linear model of traffic flow in an isolated network. Conference Publications, 2015, 2015 (special) : 670-677. doi: 10.3934/proc.2015.0670 [8] Valentin Ovsienko, Richard Schwartz, Serge Tabachnikov. Quasiperiodic motion for the pentagram map. Electronic Research Announcements, 2009, 16: 1-8. doi: 10.3934/era.2009.16.1 [9] W. G. Litvinov. Problem on stationary flow of electrorheological fluids at the generalized conditions of slip on the boundary. Communications on Pure & Applied Analysis, 2007, 6 (1) : 247-277. doi: 10.3934/cpaa.2007.6.247 [10] Jonathan Zinsl. The gradient flow of a generalized Fisher information functional with respect to modified Wasserstein distances. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 919-933. doi: 10.3934/dcdss.2017047 [11] Bendong Lou. Traveling wave solutions of a generalized curvature flow equation in the plane. Conference Publications, 2007, 2007 (Special) : 687-693. doi: 10.3934/proc.2007.2007.687 [12] Lee DeVille, Nicole Riemer, Matthew West. Convergence of a generalized Weighted Flow Algorithm for stochastic particle coagulation. Journal of Computational Dynamics, 2019, 6 (1) : 69-94. doi: 10.3934/jcd.2019003 [13] Zhitao Zhang, Haijun Luo. Symmetry and asymptotic behavior of ground state solutions for schrödinger systems with linear interaction. Communications on Pure & Applied Analysis, 2018, 17 (3) : 787-806. doi: 10.3934/cpaa.2018040 [14] Fengming Ma, Yiju Wang, Hongge Zhao. A potential reduction method for the generalized linear complementarity problem over a polyhedral cone. Journal of Industrial & Management Optimization, 2010, 6 (1) : 259-267. doi: 10.3934/jimo.2010.6.259 [15] Zhiying Qin, Jichen Yang, Soumitro Banerjee, Guirong Jiang. Border-collision bifurcations in a generalized piecewise linear-power map. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 547-567. doi: 10.3934/dcdsb.2011.16.547 [16] Alina Ostafe, Igor E. Shparlinski, Arne Winterhof. On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences. Advances in Mathematics of Communications, 2010, 4 (3) : 369-379. doi: 10.3934/amc.2010.4.369 [17] Yanxing Cui, Chuanlong Wang, Ruiping Wen. On the convergence of generalized parallel multisplitting iterative methods for semidefinite linear systems. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 863-873. doi: 10.3934/naco.2012.2.863 [18] Alireza Ghaffari Hadigheh, Tamás Terlaky. Generalized support set invariancy sensitivity analysis in linear optimization. Journal of Industrial & Management Optimization, 2006, 2 (1) : 1-18. doi: 10.3934/jimo.2006.2.1 [19] Saeed Ketabchi, Hossein Moosaei, M. Parandegan, Hamidreza Navidi. Computing minimum norm solution of linear systems of equations by the generalized Newton method. Numerical Algebra, Control & Optimization, 2017, 7 (2) : 113-119. doi: 10.3934/naco.2017008 [20] Giselle A. Monteiro, Milan Tvrdý. Generalized linear differential equations in a Banach space: Continuous dependence on a parameter. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 283-303. doi: 10.3934/dcds.2013.33.283

Impact Factor:

## Metrics

• HTML views (0)
• Cited by (0)

• on AIMS