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| Volume 8, Number 1, April 2007, pp. 105-120 | ||||||||
| Koichiro Naito and Yoshihisa Nakamura | ||||||||
| Key words: | ||||||||
| Continued fractions, Diophantine approximation, quasi-periodic orbits, fractal dimension. | ||||||||
| Mathematices Subject Classification: Primary 11A55, 11K60, 58F27, 28A80. | ||||||||
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| Abstract: | |||
| In this paper we study recurrent dimensions of discrete dynamical systems given by circle diffeomorphisms, using a renormalization method. We estimate the upper and the lower recurrent dimensions according to some algebraic properties of irrational rotation numbers of the circle mappings and we show that the gap values between the upper and the lower dimensions, which measure unpredictability levels of orbits, take positive values if the rotation numbers have good approximation properties by rational numbers. | |||
| Recurrent dimensions and Diophantine conditions of discrete dynamical systems given by circle mappings | ||