scholarly journals Exceptional Sets in Dynamical Systems and Diophantine Approximation

2002 ◽  
pp. 77-98 ◽  
Author(s):  
Maurice Dodson
Keyword(s):  
Dynamical Systems ◽  
Diophantine Approximation ◽  
Exceptional Sets

scholarly journals SHRINKING TARGETS FOR NONAUTONOMOUS DYNAMICAL SYSTEMS CORRESPONDING TO CANTOR SERIES EXPANSIONS

2015 ◽  
Vol 92 (2) ◽  
pp. 205-213 ◽  
Author(s):  
LIOR FISHMAN ◽  
BILL MANCE ◽  
DAVID SIMMONS ◽  
MARIUSZ URBAŃSKI
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Hausdorff Dimension ◽  
Diophantine Approximation ◽  
Wide Class ◽  
Series Expansions ◽  
Closed Formula ◽  
Nonautonomous Dynamical Systems ◽  
Nonautonomous Dynamical System ◽  
Cantor Series

We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the nonautonomous dynamical system on the interval$[0,1)$, viewed as$\mathbb{R}/\mathbb{Z}$, corresponding to a given method of Cantor series expansion. We also examine a wide class of examples utilising our theorem. In particular, we give a Diophantine approximation interpretation of our scheme.

scholarly journals Diophantine approximation of the orbits in topological dynamical systems

2019 ◽  
Vol 39 (5) ◽  
pp. 2455-2471
Author(s):  
Chao Ma ◽  
◽  
Baowei Wang ◽  
Jun Wu ◽  
Keyword(s):  
Dynamical Systems ◽  
Diophantine Approximation ◽  
Topological Dynamical Systems

Representation of families of sets by measures, dimension spectra and Diophantine approximation

2000 ◽  
Vol 128 (1) ◽  
pp. 111-121 ◽  
Author(s):  
K. J. FALCONER
Keyword(s):  
Dynamical Systems ◽  
Hausdorff Dimension ◽  
Diophantine Approximation ◽  
Multifractal Spectrum ◽  
Kleinian Groups ◽  
Local Dimension ◽  
Dimension Spectrum ◽  
Hyperbolic Dynamical Systems

A family of sets {Fd}d is said to be ‘represented by the measure μ’ if, for each d, the set Fd comprises those points at which the local dimension of μ takes some specific value (depending on d). Finding the Hausdorff dimension of these sets may then be thought of as finding the dimension spectrum, or multifractal spectrum, of μ. This situation pertains surprisingly often, with many familiar families of sets representable by measures which have simple dimension spectra. Examples are given from Diophantine approximation, Kleinian groups and hyperbolic dynamical systems.

Sign in / Sign up

Export Citation Format

Share Document