Abstract
A framework for the bifurcation of period-q points of iterated maps is presented. An idea of Andre Vanderbauwhede-treat period-q points of maps on Rn as zeros of an operator on Rnq is extended to include spatio-temporal symmetries and a reduced stability analysis. The framework is used to give simple proofs of results of looss and Joseph on the generic bifurcation and stability of penod-3 and period-4 points. The advantage of the tramcwork is that it allows easy generalization: allowance for degenerate bifurcations (higher multiplicity of multipliers, resonances, coefficients in normal form passing through zero) and the introduction of spatial symmetries
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