Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWebs invariant by rational maps on surfaces
74
0
0.0
(
0
)
Authors
Charles Favre
Ask ChatGPT about the research
No Arabic abstract
We prove that under mild hypothesis rational maps on a surface preserving webs are of Latt`es type. We classify endomorphisms of P^2 preserving webs, extending former results of Dabija-Jonsson.
rate research
Read More
We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by earlier authors. We can reconstruct the map from both invariants. One of the invariants defines the map unambiguously, while the other invariant also defines a new map leading to non trivial fibrations of the space of initial conditions.
We prove a new classification result for (CR) rational maps from the unit sphere in some ${mathbb C}^n$ to the unit sphere in ${mathbb C}^N$. To so so, we work at the level of Hermitian forms, and we introduce ancestors and descendants.
We develop a link between degree estimates for rational sphere maps and compressed sensing. We provide several new ideas and many examples, both old and new, that amplify connections with linear programming. We close with a list of ten open problems.
An argument is given to associate integrable nonintegrable transition of discrete maps with the transition of Lawveres fixed point theorem to its own contrapositive. We show that the classical description of nonlinear maps is neither complete nor totally predictable.
We study the geometry of the scale invariant Cassinian metric and prove sharp comparison inequalities between this metric and the hyperbolic metric in the case when the domain is either the unit ball or the upper half space. We also prove sharp distortion inequalities for the scale invariant Cassinian metric under Mobius transformations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
