相关论文: Dynamics in two complex dimensions
For the dynamics of a discontinuous map on a compact metric space, we describe an approach using suitable closed relations and connect it with the continuous dynamics on an invariant G-delta subset and with the continuous dynamics on the…
This text proposes geometrical descriptions of all variational problems invariant by conformal transformations in two variables. First a characterisation in terms of C-Finsler manifolds, a suitable generalization of Finsler manifolds, is…
This is a pedagogical exposition of holonomy groups intended for physicists. After some pertinent definitions, we focus on special holonomy manifolds, two per division algebras, and comment upon several cases of interest in physics,…
We calculate the cohomology rings of a collection of seven dimensional manifolds supporting an S^3 x S^3-action with one dimensional orbit space. These manifolds are of interest to differential geometers studying non-negative and positive…
This book offers an introduction to Hofer's metric on the group of Hamiltonian diffeomorphisms. It presents results on the diameter, geodesics, and the growth of one-parameter subgroups, along with applications to dynamics and ergodic…
This text deals with birationnal diffeomorphisms of real algebraic surfaces which have simple real dynamics and rich complex dynamics. We give an example of such a transformation on P^1xP^1, then we show that this situation is exceptional…
We study the Holomorphic and Random Dynamics of some rank 2 free groups generated by two H\'enon type maps. For these simply constructed examples we prove that the Fatou set is non-empty and that the stationary measures are supported on a…
We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown…
In \cite {HO1}, it was shown that there is a topology on $\C^2\sqcup S^3$ homeomorphic to a 4-ball such that the H\'enon mapping extends continuously. That paper used a delicate analysis of some asymptotic expansions, for instance, to…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
The phenomena that cause a value of a polynomial function to be a bifurcation one are yet to be described when the fibers have dimension higher than $1$. In this note, the main result is the construction of a polynomial submersion function…
An extension theorem for holomorphic mappings between two domains in $\mathbb C^2$ is proved under purely local hypotheses.
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
We investigate the large intersection properties of the set of points that are approximated at a certain rate by a family of affine subspaces. We then apply our results to various sets arising in the metric theory of Diophantine…
A sequence of representations \(V_n\) of the symmetric group \(S_n\) is called representation (multiplicity) stable if, after some \(n\), the irreducible decomposition of \(V_n\) stabilizes. In particular, Church, Ellenburg and Farb (2015)…
We review and investigate some new problems and results in the field of dynamical systems generated by iteration of maps, {\beta}-transformations, partitions, group actions, bundle dynamical systems, Hasse-Kloosterman maps, and some aspects…
We exhibit a family of complex manifolds, which has a member at each odd complex dimension and which has the same cohomology groups as the complex projective space at that dimension, but not homotopy equivalent to it. We also analyze the…
Based on a question raised by N. Feldman we discuss the dynamics of tuples of upper triangular Toeplitz matrices over $\mathbb{C}$. Some open problems are posed.
Given any Liouville number $\alpha$, it is shown that various subspaces are $C^\infty$-dense in the space of the orientation preserving $C^\infty$ diffeomorphisms of the circle with rotation number $\alpha$.
The McMullen-Sullivan holomorphic motion for topologically conjugate, complex polynomials with connected Julia set follows level sets of the Bottcher coordinate. The Buzzard-Verma holomorphic motion for hyperbolic, unstably connected,…