Foliations with Algebraic Limit Sets

1992 ◽  
Vol 136 (2) ◽  
pp. 429 ◽  
Author(s):  
C. Camacho ◽  
A. Lins Neto ◽  
P. Sad
Keyword(s):  

2021 ◽  
pp. 115-129
Author(s):  
Bruno Scárdua
Keyword(s):  






2000 ◽  
Vol 122 (3) ◽  
pp. 465-482 ◽  
Author(s):  
Martin Bridgeman ◽  
Edward C. Taylor


2021 ◽  
pp. 1-11
Author(s):  
STEPHEN JACKSON ◽  
BILL MANCE ◽  
SAMUEL ROTH

Abstract We consider the complexity of special $\alpha $ -limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necessarily Borel, even in the case of a surjective map on the unit square. This answers a question posed by Kolyada, Misiurewicz, and Snoha.



1994 ◽  
Vol 1 (3) ◽  
pp. 315-323
Author(s):  
František Neuman

Abstract A classification of classes of equivalent linear differential equations with respect to ω-limit sets of their canonical representatives is introduced. Some consequences of this classification to the oscillatory behavior of solution spaces are presented.



Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 452
Author(s):  
Antonio Linero-Bas ◽  
María Muñoz-Guillermo

Given a continuous Cournot map F(x,y)=(f2(y),f1(x)) defined from I2=[0,1]×[0,1] into itself, we give a full description of its ω-limit sets with non-empty interior. Additionally, we present some partial results for the empty interior case. The distribution of the ω-limits with non-empty interior gives information about the dynamics and the possible outputs of each firm in a Cournot model. We present some economic models to illustrate, with examples, the type of ω-limits that appear.



2020 ◽  
Vol 53 (2) ◽  
pp. 2039-2044
Author(s):  
Matina Baradaran ◽  
Andrew R. Teel


2009 ◽  
Vol 147 (2) ◽  
pp. 455-488 ◽  
Author(s):  
R. D. MAULDIN ◽  
T. SZAREK ◽  
M. URBAŃSKI

AbstractWe deal with contracting finite and countably infinite iterated function systems acting on Polish spaces, and we introduce conformal Graph Directed Markov Systems on Polish spaces. Sufficient conditions are provided for the closure of limit sets to be compact, connected, or locally connected. Conformal measures, topological pressure, and Bowen's formula (determining the Hausdorff dimension of limit sets in dynamical terms) are introduced and established. We show that, unlike the Euclidean case, the Hausdorff measure of the limit set of a finite iterated function system may vanish. Investigating this issue in greater detail, we introduce the concept of geometrically perfect measures and provide sufficient conditions for geometric perfectness. Geometrical perfectness guarantees the Hausdorff measure of the limit set to be positive. As a by–product of the mainstream of our investigations we prove a 4r–covering theorem for all metric spaces. It enables us to establish appropriate co–Frostman type theorems.



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