Related papers: Normal forms for contracting dynamics, revisited
We present the theory of non-stationary normal forms for uniformly contracting smooth extensions with sufficiently narrow Mather spectrum. We give coherent proofs of existence, (non)uniqueness, and a description of the centralizer results.…
This note documents the specification of normal forms in cubical type theory. The definition is already present in the proof of normalization for cubical type theory, but we present it in a more traditional style explicitly for reference.
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
We provide a brief outlook on recent developments in regularity theory for nonuniformly elliptic problems, with special emphasis on those of variational nature.
Development of theory of dynamical systems admitting the normal shift in 1993-1999 is reviewed. Basics are given with complete proofs.
Applications of the principle of reduction of couplings to the standard model and supersymmetric grand unified theories are reviewed. Phenomenological applications of renormalization group invariant sum rules for soft supersymmetry-breaking…
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
We introduce a formulation of combined systems in orthodox non-relativistic quantum mechanics, mathematically equivalent to the usual one. For context and larger issues, see http://euclid.unh.edu/~jjohnson/axiomatics.html and…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…
We discuss several aspects of the geometry of vector fields in (Poincare'-Dulac) normal form. Our discussion relies substantially on Michel theory and aims at a constructive approach to simplify the analysis of normal forms via a splitting…
The concept of unique normal form is formulated in terms of a spectral sequence. As an illustration of this technique some results of Baider and Churchill concerning the normal form of the anharmonic oscillator are reproduced. The aim of…
We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non perturbative renormalization group formalism is a promising candidate to overcome some of…
We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point purely in terms of the original Hamiltonian, avoiding the normalization procedure.…
We discuss the renormalization properties of noncommutative non-gauge supersymmetric field theories.
Newtonian dynamical systems accepting the normal shift on an arbitrary Riemannian manifold are considered. Partial differential equations forming the weak and additional normality conditions for them are reported.
We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter dependent family - via the Poincar\'e Normal Form approach. We discuss this at first formally, and…
We give an alternative method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method using tools from invariant theory to establish formulae that take symmetries into account as a starting point.…
Some properties of the inverse of the Normal distribution are studied. Its derivatives, integrals and asymptotic behavior are presented.
In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for…