A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
A survey of minimal sets

1964
*
Annales de l'Institut Fourier
*

The basic connection between

doi:10.5802/aif.160
fatcat:3ofaka4pmnhrdobzkvdooxt5wu
*almost**periodic*point and*minimal*set is this : If x e X then x is*almost**periodic*if and only if the orbit closure xT*of*x is*minimal*[12] . ... In*constructing*nonequicontinuous*minimal*sets from coset*transformation**groups*, the following theorem shows that it appears necessary to start from relatively complicated*groups*G: Let G be a*locally*...##
###
Relativized problems with abelian phase group in topological dynamics

1976
*
Proceedings of the National Academy of Sciences of the United States of America
*

Let (X, 7) be the equicontinuous

doi:10.1073/pnas.73.4.1007
pmid:16592304
pmcid:PMC430187
fatcat:7jfm4bgp7zfjbf2buudti3jqp4
*minimal**transformation**group*with X = irwZ7, the Cantor*group*, and S = z-Z2 endowed with the discrete topology acting on X by right multiplication. ... For any countable*group*Twe*construct*... equicontinuous*minimal*set with abelian phase*group*be*locally**almost**periodic*? ...##
###
Minimal sets: An introduction to topological dynamics

1958
*
Bulletin of the American Mathematical Society
*

Hence X* is an

doi:10.1090/s0002-9904-1958-10223-2
fatcat:5nu3xkhtwrbm3px32ednqxs37m
*almost**periodic**minimal*set and thus a monothetic*group*, called the structure*group**of*the original*locally**almost**periodic**minimal*set. ... Since the monothetic*groups*can be*constructed*in their entirety as the character*groups**of*the subgroups*of*the discrete circle*group*(Anzai and Kakutani 1943) [2] , the*construction*problem for*almost*...##
###
Sturmian Minimal Sets

1944
*
American Journal of Mathematics
*

We show the existence

doi:10.2307/2371769
fatcat:tnfnrwkwxzef7pxmkmig4jtlke
*of*such sets which contain asymptotic orbits, which are*locally**almost**periodic*and which are not only*minimal*under the defining*transformation*7 but are also*minimal*under every ... The simplest example*of*a*minimal*set is a*periodic*motion.*Minimal*sets which are not*periodic*motions have been*constructed*by various devices (cf. e. g., Morse [1]).’ ...##
###
Page 1309 of Mathematical Reviews Vol. 52, Issue 4
[page]

1976
*
Mathematical Reviews
*

The trans- formation

*group*(X,7) is*almost**periodic*, regularly*almost**periodic*, recursive if and only if (2*, 7) is, respectively,*almost**periodic*, regularly*almost**periodic*, recursive. L. ... Paul, Michael E. 9202*Construction**of**almost*automorphic symbolic*minimal*flows. General Topology and Appl. 6 (1976), no. 1, 45-56. ...##
###
Page 605 of American Journal of Mathematics Vol. 66, Issue 4
[page]

1944
*
American Journal of Mathematics
*

We show the existence

*of*such sets which contain asymptotic orbits, which are*locally**almost**periodic*and which are not only*minimal*under the defining*transformation*7 but are also*minimal*under every ... The simplest example*of*a*minimal*set is a*periodic*motion.*Minimal*sets which are not*periodic*motions have been*constructed*by various devices (cf. e. g., Morse [1]).’ ...##
###
Page 1955 of Mathematical Reviews Vol. 58, Issue 3
[page]

1979
*
Mathematical Reviews
*

Theorem 1: Let (7, X) be an effective

*almost**periodic**transformation**group*, where X is a compact, separable,*locally*Euclidean n-space; let J be a closed n-cell in X; then T(J) is*locally*connected. ... The author discusses various results*of*his and*of*H. Furstenberg on*minimal*sets in the context*of**transformation**groups*and, in particular,*minimal**transformation**groups*. ...##
###
Page 127 of Mathematical Reviews Vol. 2, Issue 4
[page]

1941
*
Mathematical Reviews
*

[MF 3016]
A

*group*G is called maximally (or*minimally*)*almost**periodic*if there exists for every element a distinct from the unit element e (or for no element a) an*almost**periodic*function f on G such ... Hence G; is an invariant subgroup*of*Gz generated by X and Y. M. S. Knebelman (Pullman, Wash.). v. Neumann, J. and Wigner, E. P.*Minimally**almost**periodic**groups*. ...##
###
Almost periodic functions, constructively

2005
*
Logical Methods in Computer Science
*

Here we present a simple proof

doi:10.2168/lmcs-1(3:3)2005
fatcat:5dhrmkjfxndvvkawe6qu4qtq4q
*of*Bohr's fundamental theorem for*almost**periodic*functions which we then generalize to*almost**periodic*functions on general topological*groups*. ... The*almost**periodic*functions form a natural example*of*a non-separable normed space. As such, it has been a challenge for*constructive*mathematicians to find a natural treatment*of*them. ... Parts*of*this research can already be found in my PhD-thesis [9] . I would like to thank Wim Veldman for his advice during this*period*. ...##
###
Extensions of minimal flows on manifolds

1976
*
Proceedings of the American Mathematical Society
*

*Group*extensions

*of*vector field flows for which the orbit closure map forms a fiber bundle are

*constructed*for the case

*of*

*minimal*flows on compact manifolds and compact Lie

*groups*. ... Conditions for which

*minimal*nontoral extensions exist are studied. on the left. ... Z and Y + aZ are pointwise

*almost*

*periodic*since both are G-lifts

*of*pointwise

*almost*

*periodic*

*transformation*

*groups*. ...

##
###
Extensions of Minimal Flows on Manifolds

1976
*
Proceedings of the American Mathematical Society
*

*Group*extensions

*of*vector field flows for which the orbit closure map forms a fiber bundle are

*constructed*for the case

*of*

*minimal*flows on compact manifolds and compact Lie

*groups*. ... Conditions for which

*minimal*nontoral extensions exist are studied. on the left. ... Z and Y + aZ are pointwise

*almost*

*periodic*since both are G-lifts

*of*pointwise

*almost*

*periodic*

*transformation*

*groups*. ...

##
###
Page 664 of Mathematical Reviews Vol. 35, Issue 3
[page]

1968
*
Mathematical Reviews
*

Lelek (Warsaw)
Wu, Ta-sun 3650

*Construction**of**locally**almost**periodic**minimal*trans- formation*groups*. Math. Systems Theory 1 (1967), 157-163. The author considers the following problem. ... Is there a topology » on G x J and an action*of*T on GxJ such that (1) (@xJ, ») isa compact Hausdorff space, (2) (@ x J, 7') is a*locally**almost**periodic**minimal**transformation**group*, (3) the map (g,a) ...##
###
The fundamental group and the first cohomology group of a minimal set

1963
*
Bulletin of the American Mathematical Society
*

It is further shown that for such spaces X a totally

doi:10.1090/s0002-9904-1963-10933-7
fatcat:3pioaaj4fzcepb55lgckqcuqia
*minimal*flow cannot be*locally**almost**periodic*. So on such spaces one cannot have a*locally**almost**periodic**minimal*flow. ...*almost**periodic*. ... Denoting by P the proximal relation, since X is*locally**almost**periodic*we have that P is a closed equivalence relation (see [3] ) and the induced*transformation**group*(X/P, T, 7T*) is*almost**periodic*...##
###
Embedding a transformation group in an automorphism group

1969
*
Proceedings of the American Mathematical Society
*

Leonard Shapiro has kindly pointed out that a proposition equivalent to our lemma appears in a paper

doi:10.1090/s0002-9939-1969-0244979-2
fatcat:kz6izdkm4za5napsy5v4ijdily
*of*R. Ellis ... Using a*construction**of*Baidosov [l], we show that a topological*transformation**group*with completely regular phase space X and*locally*compact phase*group*T can be equivariantly embedded in a*transformation*... The*almost**periodicity**of*(x, y) now follows from that*of*x*y by means*of*the lemma. ...##
###
Page 281 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 94, Issue 2
[page]

1960
*
American Mathematical Society. Transactions of the American Mathematical Society
*

Theorem 3 and its corollaries indicate that given a compact

*group*I, a dense subgroup 7, and a set J one should be able to*construct*the*minimal*ideal J*of*a*locally**almost**periodic**transformation**group*... An interesting problem is to provide 'XJ with a compact Hausdorff topology and to determine the action*of*T on !XJ such that (T XJ, T) is*locally**almost**periodic*. REFERENCES 1. ...
« Previous

*Showing results 1 — 15 out of 265,063 results*