Related papers: Renormalization and conjugacy of piecewise linear …
Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogues: the multidimensional quadrilateral lattices, i.e. lattices x: Z^N -> R^M, whose…
We construct renormalised models of regularity structures by using a recursive formulation for the structure group and for the renormalisation group. This construction covers all the examples of singular SPDEs which have been treated so far…
Non-renormalizable Newton maps are rigid. More precisely, we prove that their Julia set carries no invariant line fields and that the topological conjugacy is equivalent to quasi-conformal conjugacy in this case.
In this paper we introduce the notion of parabolic-like mapping, which is an object similar to a polynomial-like mapping, but with a parabolic external class, i.e. an external map with a parabolic fixed point. We prove a straightening…
In the field of the Jacobian conjecture it is well-known after Druzkowski that from a polynomial "cubic-homogeneous" mapping we can build a higher-dimensional "cubic-linear" mapping and the other way round, so that one of them is invertible…
Analytical periodic solutions for weakly Coupled Map Lattices are shown in an explicit form as well as in a recurrence relation. The results establish a link between a matricial representation and recurrence relations of the solutions.
Elementary methods are used to examine some nontrivial mathematical issues underpinning the Lorentz transformation. Its eigen-system is characterized through the exponential of a $G$-skew symmetric matrix, underlining its unconnectedness at…
Commuting maps on a class of algebras called inflated algebras are investigated. In particular, we can prove that every commuting map $\theta$ on such an algebra is of the form $\theta(x)=c x+\mu(x)$, where $c$ belongs to the base field $K$…
We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.
We suggest an extension of a certain logarithm of the total Johnson map in terms of solvable Lie groups. Here, the domain of the map is extended to a subset consisting of exponential solvable elements in the mapping class group of a…
The purpose of this short note is to clarify and present a general version of an interesting observation by Piani and Mora (Physic. Rev. A 75, 012305 (2007)), linking complete positivity of linear maps on matrix algebras to decomposability…
We study a large class of suspension semiflows which contains the Lorenz semiflows. This is a class with low regularity (merely C^{1+\alpha}) and where the return map is discontinuous and the return time is unbounded. We establish the…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
We prove that the linearization of a germ of holomorphic map of the type $F_\lambda(z)=\lambda(z+O(z^2))$ has a $ C^1$--holomorphic dependence on the multiplier $\lambda$. $C^1$--holomorphic functions are $ C^1$--Whitney smooth functions,…
Consider piecewise linear Lorenz maps on $[0, 1]$ of the following form \[ f_{a,b,c}(x)= {ll} ax+1-ac & x \in [0, c) b(x-c) & x \in (c, 1].\] We prove that $f_{a,b,c}$ admits an absolutely continuous invariant probability measure (acim)…
The generalized Lax conjecture asserts that each hyperbolicity cone is a linear slice of the cone of positive semidefinite matrices. We prove the conjecture for a multivariate generalization of the matching polynomial. This is further…
Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we…
Perturbative series of some quantities in quantum field theories, such as the pole mass of a quark, suffer from a kind of divergence called renormalon divergence. In this paper, the leading renormalon in the pole mass is investigated, and a…
A semi-analytic method to compute the first coefficients of the renormalization group functions on a random lattice is introduced. It is used to show that the two-dimensional $O(N)$ non-linear $\sigma$-model regularized on a random lattice…
We study unitarity and renormalizability in the Lifshitz scalar field theory, which is characterized by an anisotropic scaling between the space and time directions. Without the Lorentz symmetry, both the unitarity and the renormalizability…