Let f be a measure-preserving transformation of a Lebesgue space (X,μ) and let F be its extension to a bundle E = X × R by smooth fiber maps Fx : Ex → Efx so that the derivative of F at the zero section has negative Lyapunov exponents. We construct a measurable system of smooth coordinate changes Hx on Ex for μ-a.e. x so that the maps Px = Hfx ◦Fx ◦H−1 x are sub-resonance polynomials in a finit...

The concept of informational independence plays a key role in most knowledge-based systems. Although de ned di erently in di erent contexts, its basic properties have been axiomatised by J. Pearl and his co-researchers. Pearl's axiomatic system o ers a set of inference rules for deriving new independence statements from an initial set of statements and as such allows for a normal form for repre...

The system of natural deduction that originated with Gentzen (1934–5), and for which Prawitz (1965) proved a normalization theorem, is re-cast so that all elimination rules are in parallel form. This enables one to prove a very exigent normalization theorem. The normal forms that it provides have all disjunction-eliminations as low as possible, and have no major premisses for eliminations stand...

Nonlinear vector fields have two important types of singularities: the fixed points in phase space and the time singularities in the complex plane. The first singularities are locally analyzed via normal form theory whereas the second ones are studied by the Painlevé analysis. In this paper, normal form theory is used to describe the solutions around their complex-time singularities. To do so, ...

In these lectures I discuss the Linearization Theorem for Lie groupoids, and its relation to the various classical linearization theorems for submersions, foliations and group actions. In particular, I explain in some detail the recent metric approach to this problem proposed in [6]. Mathematics Subject Classification (2010). Primary 53D17; Secondary 22A22.

Since they were introduced by Poincaré in his thesis, Normal Forms have become a common and useful tool in the local qualitative study of dynamical systems. Consequently, the literature about this subject is very rich, not only because of the people working on it (Poincaré, Dulac, Birkhoff, Stenberg, Chen, Arnold, Moser, Tokarev, Bibikov, Belitskǐı, Bruno, Walcher, Cicogna, Gaeta, Bambusi and m...

This paper deals with quadratic equivalence, normal forms of observability, characteristic matrices and normal quadratic numbers for nonlinear Single-Input Single-Output (SISO) systems. We investigated both cases; nonlinear systems linearly observable and nonlinear systems with one linear unobservable mode. Particularly, the e¤ect of the normal quadratic numbers on the observer design is pointe...

—In this paper, we examine and compare de Morgan-, Kleene-, and Boolean-disjunctive and conjunctive normal forms in fuzzy settings. This generalizes papers of Turksen on the subject of Boolean-normal forms.