scholarly journals Lower bounds for the Ruelle spectrum of analytic expanding circle maps

2017 ◽  
Vol 39 (2) ◽  
pp. 289-310 ◽  
Author(s):  
OSCAR F. BANDTLOW ◽  
FRÉDÉRIC NAUD
Keyword(s):  
Lower Bounds ◽  
Blaschke Products ◽  
Expanding Maps ◽  
Circle Maps ◽  
Expanding Circle ◽  
Dense Set

We prove that there exists a dense set of analytic expanding maps of the circle for which the Ruelle eigenvalues enjoy exponential lower bounds. The proof combines potential theoretic techniques and explicit calculations for the spectrum of expanding Blaschke products.

scholarly journals Circle diffeomorphisms forced by expanding circle maps

2011 ◽  
Vol 32 (6) ◽  
pp. 2011-2024 ◽  
Author(s):  
ALE JAN HOMBURG
Keyword(s):  
Natural Extension ◽  
Skew Product ◽  
Circle Maps ◽  
Expanding Circle ◽  
Topologically Mixing ◽  
Almost All ◽  
Open Class ◽  
Product Maps ◽  
Circle Diffeomorphisms

AbstractWe discuss the dynamics of skew product maps defined by circle diffeomorphisms forced by expanding circle maps. We construct an open class of such systems that are robustly topologically mixing and for which almost all points in the same fiber converge under iteration. This property follows from the construction of an invariant attracting graph in the natural extension, a skew product of circle diffeomorphisms forced by a solenoid homeomorphism.

scholarly journals Dense Point Sets with Many Halving Lines

2019 ◽  
Vol 64 (3) ◽  
pp. 965-984
Author(s):  
István Kovács ◽  
Géza Tóth
Keyword(s):  
Discrete Comput Geom ◽  
Lower Bounds ◽  
Higher Dimensions ◽  
General Point ◽  
Point Sets ◽  
Planar Point ◽  
Dense Point ◽  
Point Set ◽  
Dense Point Set ◽  
Dense Set

Abstract A planar point set of n points is called $$\gamma $$ γ -dense if the ratio of the largest and smallest distances among the points is at most $$\gamma \sqrt{n}$$ γ n . We construct a dense set of n points in the plane with $$ne^{\Omega ({\sqrt{\log n}})}$$ n e Ω ( log n ) halving lines. This improves the bound $$\Omega (n\log n)$$ Ω ( n log n ) of Edelsbrunner et al. (Discrete Comput Geom 17(3):243–255, 1997). Our construction can be generalized to higher dimensions, for any d we construct a dense point set of n points in $$\mathbb {R}^d$$ R d with $$n^{d-1}e^{\Omega ({\sqrt{\log n}})}$$ n d - 1 e Ω ( log n ) halving hyperplanes. Our lower bounds are asymptotically the same as the best known lower bounds for general point sets.

scholarly journals Eigenfunctions for smooth expanding circle maps

Nonlinearity ◽  
2004 ◽  
Vol 17 (5) ◽  
pp. 1723-1730 ◽  
Author(s):  
Gerhard Keller ◽  
Hans Henrik Rugh
Keyword(s):  
Circle Maps ◽  
Expanding Circle

scholarly journals Mean-Field Coupling of Identical Expanding Circle Maps

2016 ◽  
Vol 164 (4) ◽  
pp. 858-889 ◽  
Author(s):  
Fanni Sélley ◽  
Péter Bálint
Keyword(s):  
Mean Field ◽  
Circle Maps ◽  
Field Coupling ◽  
Expanding Circle

scholarly journals Analytic expanding circle maps with explicit spectra

Nonlinearity ◽  
2013 ◽  
Vol 26 (12) ◽  
pp. 3231-3245 ◽  
Author(s):  
Julia Slipantschuk ◽  
Oscar F Bandtlow ◽  
Wolfram Just
Keyword(s):  
Circle Maps ◽  
Expanding Circle

scholarly journals On stochastic stability of expanding circle maps with neutral fixed points

2013 ◽  
Vol 28 (3) ◽  
pp. 423-452 ◽  
Author(s):  
Weixiao Shen ◽  
Sebastian van Strien
Keyword(s):  
Fixed Points ◽  
Stochastic Stability ◽  
Circle Maps ◽  
Expanding Circle
Sign in / Sign up

Export Citation Format

Share Document