Related papers: On the failure of linearization for germs of $C^1$…
We present various (0,2) heterotic supercurrent supermultiplets in (1+1) dimensional quantum field theories. From the minimal supercurrent supermultiplets, we deduce conditions on symmetry enhancement such as Lorentz invariance, (chiral)…
In this paper we study bilipschitz equivalences of germs of holomorphic foliations in $(\mathbb{C}^2,0)$. We prove that the algebraic multiplicity of a singularity is invariant by such equivalences. Moreover, for a large class of…
We consider H\"older continuous $GL(d,\mathbb R)$-valued cocycles, and more generally linear cocycles, over an accessible volume-preserving center-bunched partially hyperbolic diffeomorphism. We study the regularity of a conjugacy between…
In this article we show that all results proved for a large class of holomorphic germs $f : (\mathbb{C}^{n+1}, 0) \to (\mathbb{C}, 0)$ with a 1-dimension singularity in [B.II] are valid for an arbitrary such germ.
We extend the analysis of KLWMIJ evolution in terms of QCD Reggeon fields beyond leading order in the $1/N_c$ expansion. We show that there is only one type of corrections to the leading order Hamiltonian discussed in \cite{last}. These are…
We examine spacetimes which generalize Lifshitz scaling to allow hyperscaling violation invariance (i.e. a constant conformal transformation) for the types of singularities frequently found in the Lifshitz case. We find that most of these…
In this paper we study the centralizer $C(X)$ of a germ of vector field at $0\in\C^n$. A particular atention is given to the case of dimension two.
We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computer-free proof of the original Feigenbaum observation of the universal parameter…
We continue the study in [21] of the linearizability near an indif- ferent fixed point of a power series f, defined over a field of prime characteristic p. It is known since the work of Herman and Yoccoz [13] in 1981 that Siegel's…
This article is concerned with the geometry of germs of real analytic surfaces in $(\mathbb{C}^2,0)$ having an isolated Cauchy-Riemann (CR) singularity at the origin. These are perturbations of {\it Bishop quadrics}. There are two kinds of…
We construct a family of hyperbolic string vertices in the oriented open-closed string field theory, generalizing the recent result on hyperbolic closed string vertices by Costello and Zwiebach. The vertices are described by certain…
In this paper we extend M. Lyubich's recent results on the global hyperbolicity of renormalization of quadratic-like germs to the space of C^r unimodal maps with quadratic critical point. We show that in this space the bounded-type limit…
We consider H\"older continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $M$. We obtain several results for this setting. If a cocycle is bounded in…
We introduce a class of "Lipschitz horizontal" vector fields in homogeneous groups, for which we show equivalent descriptions, e.g. in terms of suitable derivations. We then investigate the associated Cauchy problem, providing a uniqueness…
We study cohomology groups of the Lie algebra of vector fields on the complex line, $W_1$, with values in the tensor fields in several variables. From a generalization by Scheja of the second Riemann (Hartogs) continuation theorem, we…
The famous MLC Conjecture states that the Mandelbrot set is locally connected, and it is considered by many to be the central conjecture in one-dimensional complex dynamics. Among others, it implies density of hyperbolicity in the quadratic…
We consider C^{2} Henon-like families of diffeomorphisms of R^{2} and study the boundary of the region of parameter values for which the nonwandering set is uniformly hyperbolic. Assuming sufficient dissipativity, we show that the loss of…
We give an explicit description of hyperbolic Reinhardt domains D in C^2 such that: (i) D has C^k-smooth boundary for some k greater than or equal to 1, (ii) D intersects at least one of the coordinate complex lines $\{z_1=0\}$,…
We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by a similar property of the fundamental group of the complement of an irreducible hypersurface in the complex projective…
The theory of circuit quantum electrodynamics has successfully analyzed superconducting circuits on the basis of the classical Lagrangian, and the corresponding quantized Hamiltonian, describing these circuits. In many simplified versions…