scholarly journals Derivatives not first return integrable on a fractal set

2018 ◽  
Vol 67 (2) ◽  
pp. 597-604
Author(s):  
Donatella Bongiorno
Keyword(s):  
Fractal Set

scholarly journals Furstenberg sets for a fractal set of directions

2012 ◽  
Vol 140 (8) ◽  
pp. 2753-2765 ◽  
Author(s):  
Ursula Molter ◽  
Ezequiel Rela
Keyword(s):  
Fractal Set

scholarly journals Fractal Flux Tubes of the Solar Magnetic Field

1991 ◽  
Vol 130 ◽  
pp. 140-146 ◽  
Author(s):  
Alexander Ruzmaikin ◽  
Dmitry Sokoloff ◽  
Theodore Tarbell
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Magnetic Structure ◽  
Solar Magnetic Field ◽  
Dynamo Model ◽  
Small Scale ◽  
Flux Tubes ◽  
Fractal Set ◽  
Fractal Distribution ◽  
Linear Resolution

Abstract The small-scale solar magnetic field exceeding a given threshold forms a fractal set. A dimension of this fractal is found from magnetograms with varying linear resolution. The dimension depends on the value of the threshold magnetic field (multifractality). A simple dynamo model explaining the origin of the fractal magnetic structure is considered. The dynamo produces a magnetic field in the form of flux tubes with a fractal distribution of magnetic field across the tube. The observed dimension gives a possibility of estimating a degree of structuredness of the solar velocity field.

scholarly journals Do Arnold tongues really constitute a fractal set?

2010 ◽  
Vol 246 ◽  
pp. 012031
Author(s):  
A L Gama ◽  
M S Teixeira de Freitas
Keyword(s):  
Fractal Set ◽  
Arnold Tongues

SCALING BEHAVIOUR OF A MULTIPLY CONNECTED FLUCTUATING INTERFACE IN TWO DIMENSIONS

Fractals ◽  
2003 ◽  
Vol 11 (supp01) ◽  
pp. 227-232
Author(s):  
AYŞE ERZAN ◽  
HÜSEY.IN KAYA ◽  
ALKAN KABAKÇIOĞLU
Keyword(s):  
Kinetic Model ◽  
Numerical Simulations ◽  
Average Velocity ◽  
Two Dimensions ◽  
Scaling Exponents ◽  
Multiply Connected ◽  
Fractal Set ◽  
Scaling Behaviour ◽  
Infinite String

We consider a one-parameter kinetic model for a fluctuating interface which can be thought of as an infinite string decorated with infinitely many closed strings. Numerical simulations show that a number of scaling exponents describing this string system may be related to the Kardar-Parisi-Zhang exponents. However, as the average velocity of the infinite string is taken to zero, and the string system becomes an isotropic fractal set, we also find new exponents which cannot be reduced to previously known ones.

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