1 research outputs found
On a differentiable linearization theorem of Philip Hartman
A linear automorphism of Euclidean space is called bi-circular its
eigenvalues lie in the disjoint union of two circles and in the
complex plane where the radius of is , the radius of is ,
and . A well-known theorem of Philip Hartman states that a
local diffeomorphism of Euclidean space with a fixed point
whose derivative is bi-circular is linearizable near .
We generalize this result to diffeomorphisms where . We also extend the result to local diffeomorphisms in Banach
spaces with bump functions. The results apply to give simpler
proofs under weaker regularity conditions of classical results of L. P.
Shilnikov on the existence of horseshoe dynamics near so-called saddle-focus
critical points of vector fields in .Comment: This May 16, 2017 revision corrects some typos and makes some minor
changes in the exposition. It is the actual version soon to be publishe