Counting Hyperbolic Components
Jan Kiwi, Mary Rees
TL;DR
This paper provides formulas to count specific types of hyperbolic components in the parameter space of quadratic rational maps, based on the periods of their attracting cycles.
Contribution
It introduces explicit formulas for enumerating type II and type IV hyperbolic components for all fixed periods of attractive cycles.
Findings
Formulas for counting hyperbolic components are derived.
Counts are provided for all fixed periods of attractive cycles.
The results advance understanding of the structure of quadratic rational maps.
Abstract
We give formulas for the numbers of type II and type IV hyperbolic components in the space of quadratic rational maps, for all fixed periods of attractive cycles.
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