scholarly journals Connecting Orbit Structure of Monotone Solutions in the Shadow System

1997 ◽  
Vol 140 (2) ◽  
pp. 309-364 ◽  
Author(s):  
Hiroshi Kokubu ◽  
Konstantin Mischaikow ◽  
Yasumasa Nishiura ◽  
Hiroe Oka ◽  
Takeshi Takaishi
Keyword(s):  
Shadow System ◽  
Orbit Structure ◽  
Connecting Orbit ◽  
Monotone Solutions

scholarly journals The absorption theorem for affable equivalence relations

2008 ◽  
Vol 28 (5) ◽  
pp. 1509-1531 ◽  
Author(s):  
THIERRY GIORDANO ◽  
HIROKI MATUI ◽  
IAN F. PUTNAM ◽  
CHRISTIAN F. SKAU
Keyword(s):  
Dynamical Systems ◽  
Equivalence Relation ◽  
Closed Subset ◽  
Cantor Set ◽  
Equivalence Relations ◽  
Orbit Structure ◽  
Orbit Equivalent ◽  
Finite Set ◽  
Significant Generalization

AbstractWe prove a result about extension of a minimal AF-equivalence relation R on the Cantor set X, the extension being ‘small’ in the sense that we modify R on a thin closed subset Y of X. We show that the resulting extended equivalence relation S is orbit equivalent to the original R, and so, in particular, S is affable. Even in the simplest case—when Y is a finite set—this result is highly non-trivial. The result itself—called the absorption theorem—is a powerful and crucial tool for the study of the orbit structure of minimal ℤn-actions on the Cantor set, see Remark 4.8. The absorption theorem is a significant generalization of the main theorem proved in Giordano et al [Affable equivalence relations and orbit structure of Cantor dynamical systems. Ergod. Th. & Dynam. Sys.24 (2004), 441–475] . However, we shall need a few key results from the above paper in order to prove the absorption theorem.

scholarly journals Mass Distribution of the E0 Galaxy NGC 6703 from Absorption Line Profile Kinematics

1999 ◽  
Vol 186 ◽  
pp. 189-190
Author(s):  
O.E. Gerhard ◽  
G. Jeske ◽  
R.P. Saglia ◽  
Ralf Bender
Keyword(s):  
Dark Matter ◽  
Absorption Line ◽  
Mass Distribution ◽  
Line Profile ◽  
Elliptical Galaxies ◽  
Velocity Profiles ◽  
Matter Content ◽  
Orbit Structure ◽  
Extensive Analysis ◽  
Preliminary Account

Absorption line velocity profiles (vps) contain important information on the anisotropy and mass distribution of elliptical galaxies (e.g., Gerhard 1993, Merritt 1993). Here we briefly present results of an extensive analysis of the E0 galaxy NGC 6703 (Gerhard et al. 1997). This work is part of an observational and theoretical program aimed at understanding the orbit structure and dark matter content of ellipticals at intermediate radii (a preliminary account is given in Saglia et al. 1997).

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