Wang Zhiqiang
In this paper,we introduce a Zp index theory.For any given positive integer p,we introduce a subset Ep of positive integers and define a family of index mappings σn,∀n∈Ep.We prove that this index theory possesses the similar properties as Z2 and S1 index theories do.In particular,by means of a Zp Borsuk-Ulam theorem given in one of our recent papers we prove that under some suitable conditions this theory also possesses dimensional property which is important in applications.As a simple application,we study the bifurcation problem of periodic solutions of nonautonomous Hamiltonian systems.