Diagonalization of non-diagonalizable discrete holomorphic dynamical systems
Marco Abate
Abstract
We describe a canonical procedure for associating to any (germ of) holomorphic self-map f of Cn fixing the origin such that dfO is invertible and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p from M to Cn, a point e in M and a (germ of) holomorphic self-map F of M so that: p restricted to the complement of p-1(O) is a biholomorphism between this complement and Cn minus the origin; p semiconjugates f and F; and e is a fixed point of F such that dFe is diagonalizable. Furthermore, we use this construction to describe the local dynamics of such an f nearby the origin when the only eigenvalue of dfO is 1.
Create a lesson
Related papers
Square Functions and the Complete Crouzeix Conjecture in Dimension Three
Per Åhag, Rafał Czyż, Antti Perälä et al.
On the Levi map of nondegenerate CR submanifolds
Florian Bertrand, Francine Meylan
Smale's Mean Value Conjecture and its Dual Conjecture for Complex Polynomials
Aneesh Jatar, Tuen Wai Ng
Transcendental Numerical Dimension and Rational Quotients in Kähler Geometry
Songchen Liu
Compactness and the essential norm on Bergman spaces of the Siegel upper half-space
Peiyao Li, Congwen Liu, Jiajia Si
Existence of a "maximal" domain of meromorphy for an analytic function outside a polar compact set
Aleksandr Komlov