This issuePrevious ArticleInduced maps of hyperbolic Bernoulli systemsNext ArticleSRB measures of certain almost hyperbolic diffeomorphisms with a tangency
Normal forms for semilinear functional differential equations in Banach spaces and applications. Part II
A normal form theory for
functional differential equations in Banach spaces
of retarded type is addressed. The theory is based on a formal
adjoint theory for the linearized equation at an equilibrium
and on the existence of center manifolds for perturbed inhomogeneous equations,
established in the first part of this work
under weaker hypotheses than those
that usually appear
in the literature.
Based on these results, an algorithm to compute normal forms on finite
dimensional invariant manifolds of
the origin is
presented. Such normal forms are important in obtaining the ordinary
differential equation
giving the flow on center manifolds explicitly in terms of the original
functional differential equation. Applications to Bogdanov-Takens and Hopf
bifurcations are
presented.