By David H. Sattinger
A dialogue of advancements within the box of bifurcation thought, with emphasis on symmetry breaking and its interrelationship with singularity idea. The notions of common strategies, symmetry breaking, and unfolding of singularities are mentioned intimately. The ebook not just reports contemporary mathematical advancements but in addition presents a stimulus for additional examine within the box.
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Additional resources for Branching in the Presence of Symmetry
17) possesses infinitely many T-periodic solutions. Rabinowitz  had previously shown that systems of the type z = /VHz(t, z) possess at least one T-periodic solution if H(t, z) is a T-periodic bounded perturbation of a super quadratic Hamiltonian H(z). Bahri and Berestycki have derived similar results for the inhomogeneous boundary value problem In order to obtain their results, they applied a topological perturbation method developed by Bahri . Consider the perturbed functional on the sphere ||u|| = l (||u|l is the Dirichlet norm of u).
There is a natural group action induced on T'(M) given by
For example, the spherical harmonics Ylm(6,
Branching in the Presence of Symmetry by David H. Sattinger