434 research outputs found
Non-imprisonment conditions on spacetime
The non-imprisonment conditions on spacetimes are studied. It is proved that
the non-partial imprisonment property implies the distinction property.
Moreover, it is proved that feeble distinction, a property which stays between
weak distinction and causality, implies non-total imprisonment. As a result the
non-imprisonment conditions can be included in the causal ladder of spacetimes.
Finally, totally imprisoned causal curves are studied in detail, and results
concerning the existence and properties of minimal invariant sets are obtained.Comment: 12 pages, 2 figures. v2: improved results on totally imprisoned
curves, a figure changed, some misprints fixe
Compactness of the space of causal curves
We prove that the space of causal curves between compact subsets of a
separable globally hyperbolic poset is itself compact in the Vietoris topology.
Although this result implies the usual result in general relativity, its proof
does not require the use of geometry or differentiable structure.Comment: 15 page
A convergence on Boolean algebras generalizing the convergence on the Aleksandrov cube
We compare the forcing related properties of a complete Boolean algebra B
with the properties of the convergences (the algebraic convergence)
and on B generalizing the convergence on the Cantor and
Aleksandrov cube respectively. In particular we show that is a
topological convergence iff forcing by B does not produce new reals and that
is weakly topological if B satisfies condition
(implied by the -cc). On the other hand, if is a
weakly topological convergence, then B is a -cc algebra or in
some generic extension the distributivity number of the ground model is greater
than or equal to the tower number of the extension. So, the statement "The
convergence on the collapsing algebra B=\ro
((\omega_2)^{<\omega}) is weakly topological" is independent of ZFC
On two-dimensional surface attractors and repellers on 3-manifolds
We show that if is an -diffeomorphism with a surface
two-dimensional attractor or repeller and is a
supporting surface for , then and
there is such that: 1) is a union
of disjoint tame surfaces such that every is
homeomorphic to the 2-torus . 2) the restriction of to
is conjugate to Anosov automorphism of
Functions of several Cayley-Dickson variables and manifolds over them
Functions of several octonion variables are investigated and integral
representation theorems for them are proved. With the help of them solutions of
the -equations are studied. More generally functions of
several Cayley-Dickson variables are considered. Integral formulas of the
Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are
proved in the new generalized form for functions of Cayley-Dickson variables
instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson
graded algebras are defined and investigated
Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers
In this paper we study the ergodic properties of mathematical billiards
describing the uniform motion of a point in a flat torus from which finitely
many, pairwise disjoint, tubular neighborhoods of translated subtori (the so
called cylindric scatterers) have been removed. We prove that every such system
is ergodic (actually, a Bernoulli flow), unless a simple geometric obstacle for
the ergodicity is present.Comment: 24 pages, AMS-TeX fil
On extending actions of groups
Problems of dense and closed extension of actions of compact transformation
groups are solved. The method developed in the paper is applied to problems of
extension of equivariant maps and of construction of equivariant
compactifications
The dimension of the space of R-places of certain rational function fields
We prove that the space of -places of the field
of rational functions of two variables with coefficients in a totally
Archimedean field has covering and integral dimensions \dim
M(K(x,y))=\dim_\IZ M(K(x,y))=2 and the cohomological dimension for any Abelian 2-divisible coefficient group .Comment: 8 page
Groups of diffeomorphisms and geometric loops of manifolds over ultra-normed fields
The article is devoted to the investigation of groups of diffeomorphisms and
loops of manifolds over ultra-metric fields of zero and positive
characteristics. Different types of topologies are considered on groups of
loops and diffeomorphisms relative to which they are generalized Lie groups or
topological groups. Among such topologies pairwise incomparable are found as
well. Topological perfectness of the diffeomorphism group relative to certain
topologies is studied. There are proved theorems about projective limit
decompositions of these groups and their compactifications for compact
manifolds. Moreover, an existence of one-parameter local subgroups of
diffeomorphism groups is investigated.Comment: Some corrections excluding misprints in the article were mad
On the Lebesgue measure of Li-Yorke pairs for interval maps
We investigate the prevalence of Li-Yorke pairs for and
multimodal maps with non-flat critical points. We show that every
measurable scrambled set has zero Lebesgue measure and that all strongly
wandering sets have zero Lebesgue measure, as does the set of pairs of
asymptotic (but not asymptotically periodic) points.
If is topologically mixing and has no Cantor attractor, then typical
(w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally
admits an absolutely continuous invariant probability measure (acip), then
typical pairs have a dense orbit for . These results make use of
so-called nice neighborhoods of the critical set of general multimodal maps,
and hence uniformly expanding Markov induced maps, the existence of either is
proved in this paper as well.
For the setting where has a Cantor attractor, we present a trichotomy
explaining when the set of Li-Yorke pairs and distal pairs have positive
two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure
- …