Topological classification of structurally stable 3-diffeomorphisms with two-dimensional basis sets
In this paper a unified method for studying foliations with transversal parabolic geometry of rank one is presented.
Ideas of Fraces' paper on parabolic geometry of rank one and of works of the author on conformal foliations
We investigated conformal foliations $(M,F)$ of codimension $q\geq 3$ and proved a criterion for them to be Riemannian. In particular, the application of this criterion allowed us to proof the existence of an attractor that is a minimal set for each non-Riemannian conformal foliation. Moreover, if foliated manifold is compact then non-Riemannian conformal foliation $(M,F)$ is $(Conf(S^q),S^q)$-foliation with finitely many minimal sets. They are all attractors, and each leaf of the foliation belongs to the basin of at least one of them. The specificity of the proper conformal foliations is indicated. Special attention is given to complete conformal foliations.
An attractor, in complex systems theory, is any state that is more easily or more often entered or acquired than departed or lost; attractor states therefore accumulate more members than non-attractors, other things being equal. In the context of language evolution, linguistic attractors include sounds, forms, and grammatical structures that are prone to be selected when sociolinguistics and language contact make it possible for speakers to choose between competing forms. The reasons why an element is an attractor are linguistic (auditory salience, ease of processing, paradigm structure, etc.), but the factors that make selection possible and propagate selected items through the speech community are non-linguistic. This paper uses the consonants in personal pronouns to show what makes for an attractor and how selection and diffusion work, then presents a survey of several language families and areas showing that the derivational morphology of pairs of verbs like fear and frighten, or Turkish korkmak 'fear, be afraid' and korkutmak 'frighten, scare', or Finnish istua 'sit' and istutta 'seat (someone)', or Spanish sentarse 'sit down' and sentar 'seat (someone)' is susceptible to selection. Specifically, the Turkish and Finnish pattern, where 'seat' is derived from 'sit' by addition of a suffix-is an attractor and a favored target of selection. This selection occurs chiefly in sociolinguistic contexts of what is defined here as linguistic symbiosis, where languages mingle in speech, which in turn is favored by certain demographic, sociocultural, and environmental factors here termed frontier conditions. Evidence is surveyed from northern Eurasia, the Caucasus, North and Central America, and the Pacific and from both modern and ancient languages to raise the hypothesis that frontier conditions and symbiosis favor causativization.
In this paper we study attractors of skew products, for which the following dichotomy is ascertained. These attractors either are not asymptotically stable or possess the following two surprising properties. The intersection of the attractor with some invariant submanifold does not coincide with the attractor of the restriction of the skew product to this submanifold but contains this restriction as a proper subset. Moreover, this intersection is thick on the submanifold, that is, both the intersection and its complement have positive relative measure. Such an intersection is called a bone, and the attractor itself is said to be bony. These attractors are studied in the space of skew products. They have the important property that, on some open subset of the space of skew products, the set of maps with such attractors is, in a certain sense, prevalent, i. e., "big." It seems plausible that attractors with such properties also form a prevalent subset in an open subset of the space of diffeomorphisms.