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Hopf bifurcation with zero frequency and imperfect SO(2) symmetry
Hopf bifurcation zero frequency imperfect SO(2) symmetry Dynamical Systems
2012/6/29
Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dy...
Asymptotic stability of ground states in some Hamiltonian PDEs with symmetry
Asymptotic stability of ground states Hamiltonian PDEs symmetry
2011/9/22
Abstract: We consider a ground state (soliton) of a Hamiltonian PDE. We prove that if the soliton is orbitally stable then it is also asymptotically stable. The main assumptions are transversal nondeg...
Applications of Classical Scaling Symmetry
Classical Scaling Symmetry second-order differential equation conservation laws central field dynamics
2011/7/7
Any symmetry reduces a second-order differential equation to a first-order equation: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetr...
The continuous symmetries of physical systems are reflected not only by conservation laws, but also by constraints on the probability, or particle dis-tribution functions, and phase-space reduction.