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- W2516696393 abstract "We are concerned with finitely nested square roots which are roots of iterations of a real quadratic polynomial $x^2-c$ with $cgeq 2$, and the limits of such nested square roots. We investigate how they are related to a Poincare function $f(x)$ satisfying the functional equation $f(sx)=f(x)^2-c$, where $s=1+sqrt{1+4c}$. Our main theorems can be viewed as a natural generalization of the work of Wiernsberger and Lebesgue for the case $c=2$. The key ingredients of the proof are some analytic properties of $F(x)$, which have been intensively studied by the second author using infinite compositions." @default.
- W2516696393 created "2016-09-16" @default.
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- W2516696393 date "2016-06-01" @default.
- W2516696393 modified "2023-10-17" @default.
- W2516696393 title "Nested Square Roots and Poincaré Functions" @default.
- W2516696393 doi "https://doi.org/10.3836/tjm/1471873313" @default.
- W2516696393 hasPublicationYear "2016" @default.
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