Analytic Automorphisms and Transitivity of Analytic Mappings

Discrete-time Transitivity and Accessibility: Analytic Systems

A basic open question for discrete-time nonlinear systems is that of determining when, in analogy with the classical continuous-time “positive form of Chow’s Lemma,” accessibility follows from transitivity of a natural group action. This paper studies the problem, and establishes the desired implication for analytic systems in several cases: (i) compact state space, (ii) under a Poisson stabili...

Complex Analytic Mappings

Analytic Mappings on Hyperfinite Sets

Let S and T be hyperfinite sets in an N]-saturated nonstandard universe. The following are equivalent: m 1*1 ~ l (l) rff ~ • • (ii) There is a bijection from 5 onto T whose graph is Borel (over the internal subsets of S x T). This follows from somewhat more general results about analytic partial functions on hyperfinite sets, the proofs of which use Choquet's theorem on the capacitibility of an...

Analytic combinatory calculi and the elimination of transitivity

We introduce, in a general setting, an “analytic” version of standard equational calculi of combinatory logic. Analyticity lies on the one side in the fact that these calculi are characterized by the presence of combinatory introduction rules in place of combinatory axioms, and on the other side in that the transitivity rule proves to be eliminable. Apart from consistency, which follows immedia...

GERMS OF LOCAL AUTOMORPHISMS OF REAL-ANALYTIC CR STRUCTURES AND ANALYTIC DEPENDENCE ON k-JETS

The topic of the paper is the study of germs of local holomorphisms f between Cn and Cn ′ such that f(M) ⊂ M ′ and df(T cM) = T cM ′ for M ⊂ Cn and M ′ ⊂ Cn generic real-analytic CR submanifolds of arbitrary codimensions. It is proved that for M minimal and M ′ finitely nondegenerate, such germs depend analytically on their jets. As a corollary, an analytic structure on the set of all germs of ...