Related papers: Henon-like maps with arbitrary stationary combinat…

The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of asymptotically holomorphic extensions of $C^r$ ($r>3$)…

We show that for all Cantor set $K_1$ on ${\mathbb R}^d$, it is always possible to find another Cantor set $K_2$ so that the sum $g(K_1)+ K_2$ (where $g$ is a $C^1$ local diffeomorphism) has non-empty interior, and the existence of the…

We propose global surjectivity theorems of differentiable maps based on second order conditions. Using the homotopy continuation method, we demonstrate that, for a $C^2$ differentiable map from a Hilbert space to a finite-dimensional…

In this article we investigate stationary cKdV systems and prove that every $N$-field stationary cKdV system can be written, after a careful reparametrization of jet variables, as a classical separable St\"ackel system on $N+1$ different…

We prove that $2$-dimensional $Q$-valued maps that are stationary with respect to outer and inner variations of the Dirichlet energy are H\"older continuous and that the dimension of their singular set is at most one. In the course of the…

Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…

Maps are polygonal cellular networks on Riemann surfaces. This paper analyzes the construction of closed form general representations for the enumerative generating functions associated to maps of fixed but arbitrary genus. The method of…

Given any cancellative monoid $\mathcal{M}$, we study the Hankel system determined by its multiplication table. We prove that the Hankel system admits self-absorption property provided that the monoid $\mathcal{M}$ has the local algebraic…

We present preliminary results of a non-perturbative study of the scale-dependent renormalization constants of a complete basis of Delta F=2 parity-odd four-fermion operators that enter the computation of hadronic B-parameters within the…

We investigate the spectral consequences of the uniquely determined Hermitian ordering of the Dirac Hamiltonian with spatially varying mass. In contrast to the nonrelativistic case, where continuous families of admissible prescriptions…

We extend many known results for harmonic maps from the 2-sphere into a Grassmannian to harmonic maps of finite uniton number from an arbitrary Riemann surface. Our method relies on a new theory of nilpotent cycles arising from the diagrams…

We show that for a class of $C^2$ quasiperiodic potentials and for any Diophantine frequency, the spectrum of the corresponding Schr\"odinger operators is Cantor. Our approach is of purely dynamical systems, which depends on a detailed…

A noncommutative Feynman graph is a ribbon graph and can be drawn on a genus $g$ 2-surface with a boundary. We formulate a general convergence theorem for the noncommutative Feynman graphs in topological terms and prove it for some classes…

By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs), which take the form $\int dx\, f(x) \mathcal{H}(x)$, where $\mathcal{H}(x)$ is the Hamiltonian density…

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…

For a non-flat $C^3$ unimodal map with a Cantor attractor, we show that for any open cover $\mathcal U$ of this attractor, the complexity function $p(\mathcal U, n)$ is of order $n\log n$. In the appendix, we construct a non-renormalizable…

It is well-known that the Julia set of a hyperbolic rational map is quasisymmetrically equivalent to the standard Cantor set. Using the uniformization theorem of David and Semmes, this result comes down to the fact that such a Julia set is…

For every compact Kaehler manifold we give a canonical extension of Griffith's period map to generalized deformations, intended as solutions of Maurer-Cartan equation in the algebra of polyvector fields. Our construction involves the notion…

Let $H$ and $K$ be two complex inner product spaces with dim$(X)\geq 2$. We prove that for each non-zero additive mapping $A:H \to K$ with dense image the following statements are equivalent: $(a)$ $A$ is (complex) linear or…

We define a hyperbolic renormalizations suitable for maps of small determinant, with uniform bounds for large periods. The techniques involve an improvement of the celebrated Palis-Takens renormalization and normal forms (fibered…