The ON SOME PROPERTIES OF CONTINUED FRACTIONS AND RETURN TIME FOR CIRCLE HOMEOMORPHISMS
Keywords:
circle homeomorphism, break point, rotation number, continued fractions, return timeAbstract
In present work we study general properties of continued fractions and the return times for circle homeomorphisms with irrational rotation number. Consider the set $X$ of all orientation preserving circle homeomorphisms $T$ with one break point and irrational rotation number. There are given proof of the main theorem for return time using visualizations and constructed example to computing return time for irrational rotation number.
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