# Springer Research Monograph

## Singularity Theory and Equivariant Symplectic Maps

The monograph presents new results on bifurcations of symplectic maps and a singularity theory framework for equivariant gradient bifurcation problems.
 Topics * Generic bifurcation of periodic points + maps on R^{2n}: a Lagrangian variational formulation + new proof of Meyer's Theorem on periodic points + reduced stability of bifurcating period-q points * Periodic points of equivariant symplectic maps + subharmonic bifurcation of equivariant symplectic maps + O(2)-equivariant symplectic maps + parametrically forced spherical pendulum + Orbit space reduction for symplectic maps + symmetries and Noether's Theorem for maps * Singularity theory for equivariant gradient maps + classification of Z_q- and D_q-equivariant gradient maps + classification of degenerate bifurcations of maps * Collision of Floquet multipliers on the unit circle + "Hamiltonian-Hopf bifurcation" for symplectic maps + Generic theory for symplectic maps near rational collision + collision of multipliers at +/- i + reduced stability results for bifurcations near collisions + generic theory for maps near a collision at irrational points + effect of symmetry on maps with collisions * Some Appendices + signature on configuration space + equivariant splitting lemma + about reversible-symplectic maps + twist maps and dynamical equivalence + instability lemma + (p,q)-resonances for symplectic maps + isotropy and twisted subgroups of \Sigma\times Z_q + about symmetric symplectic operators