Mass endomorphisms, surgery and perturbations

Perturbations D’exemples De Lattès Et Dimension De Hausdorff Du Lieu De Bifurcation

We give an estimate for the Hausdorff dimension of the bifurcation locus of a family of endomorphisms of Pk(C). This dimension is maximal near isolated Lattès examples.

Quasicompact and Riesz unital endomorphisms of real Lipschitz algebras of complex-valued functions

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

Parabolic Implosion for Endomorphisms of C2

Parabolic dynamics and the study of parabolic perturbations have been at the heart of holomorphic dynamics in the last couple of decades. Starting with the work by Lavaurs [Lav89], the theory of parabolic implosion has provided useful tools for a very precise control of these perturbations and for the proof of some of the most striking recent results in the field, e.g., the construction of Juli...

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

Mass endomorphism, surgery and perturbations

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.