Related papers: A Poincar\'e-Dulac renormalization theorem for att…
In this revised version, applying a general renormalization procedure for formal self-maps, producing a formal normal form simpler than the classical Poincar\'e-Dulac normal form, we shall give a complete list of normal forms for…
Following Favre, we define a holomorphic germ f:(C^d,0) -> (C^d,0) to be rigid if the union of the critical set of all iterates has simple normal crossing singularities. We give a partial classification of contracting rigid germs in…
The goal of this paper is to study the dynamics of holomorphic diffeomorphisms in C^n such that the resonances among the first 1<= r<= n eigenvalues of the differential are generated over N by a finite number of Q-linearly independent…
Dimensional Resonance Theory proposes that gravity and fundamental forces can be interpreted as emergent phenomena arising from three-dimensional waves (3D) projected onto lower dimensions. To test the internal consistency of this proposal,…
The quantum field theory describing electric and magnetic charges and revealing a dual symmetry was developed in the Zwanziger formalism. The renormalization group (RG) equations for both fine structure constants - electric $\alpha$ and…
We present a geometric proof of the Poincar\'e-Dulac Normalization Theorem for analytic vector fields with singularities of Poincar\'e type. Our approach allows us to relate the size of the convergence domain of the linearizing…
Let $f$ be a germ of biholomorphism of $\C^n$, fixing the origin. We show that if the germ commutes with a torus action, then we get information on the germs that can be conjugated to $f$, and furthermore on the existence of a holomorphic…
We give a simple example of a polynomial contraction automorphism of $\mathbb C^d$, $ d\ge 3 $, with unbounded degree growth. Combined with Poincar\'e-Dulac theorem it provides an algebraic automorphism of $\mathbb C^d$, $ d\ge 3 $, which…
We study the sequence of attraction rates of iterates of a dominant superattracting holomorphic fixed point germ f:(C^2,0)->(C^2,0). By using valuative techniques similar to those developed by Favre-Jonsson, we show that this sequence…
We show that a nonlinear dynamical system in Poincare'-Dulac normal form (in $\R^n$) can be seen as a constrained linear system; the constraints are given by the resonance conditions satisfied by the spectrum of (the linear part of) the…
The paper deals with dynamics of expanding Lorenz maps, which appear in a natural way as Poincar\`e maps in geometric models of well-known Lorenz attractor. Using both analytical and symbolic approaches, we study connections between…
Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in C^n whose differentials have one-dimensional family of resonances in the first m eigenvalues, m <= n (but more resonances are allowed…
In this paper we study the existence of basins of attraction for germs of 2-resonant biholomorphisms of $\C^n$ fixing a point, that is germs such that the eigenvalues of the differential at the fixed point have a 2 dimensional family of…
We study holomorphic germs $f:(\mathbb{C}^2, 0) \rightarrow (\mathbb{C}^2,0) with non-invertible differential $df_0$. In order to do this, we search for a modification $\pi:X \rightarrow (\mathbb{C}^2,0)$ (i.e., a composition of point…
A single spin-$\frac{1}{2}$ particle obeys the Dirac equation in $d\ge 1$ spatial dimension and is bound by an attractive central monotone potential which vanishes at infinity (in one dimension the potential is even). This work refines the…
A functional renormalization group approach to $d$-dimensional, $N$-component, non-collinear magnets is performed using various truncations of the effective action relevant to study their long distance behavior. With help of these…
We prove essential self-adjointness of Dirac operators with Lorentz scalar potentials which grow sufficiently fast near the boundary $\partial\Omega$ of the spatial domain $\Omega\subset\mathbb R^d$. On the way, we first consider general…
Poincar\'e Gauge Theories are a class of Metric-Affine Gravity theories with a metric-compatible (i.e. Lorentz) connection and with an action quadratic in curvature and torsion. We perform an explicit one-loop calculation starting with a…
The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective…
We study the thermodynamic properties of the two-component $2+1$-dimensional massive Dirac fermions in an external magnetic field. The broken time-reversal symmetry results in the presence of a linear in the magnetic field part of the…