Difference between revisions of "Principal Abel function"
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| − | The principal Abel function (up to an additive constant) of $f$ at fixpoint $a$ is the [[Abel function]] of $f$ such that the [[fractional | + | The principal Abel function (up to an additive constant) of $f$ at fixpoint $a$ is the [[Abel function]] of $f$ such that the [[fractional iterate]]s $\phi_c$ defined by |
| − | $$\ | + | $$\phi_c(x) = \alpha^{-1}(c+\alpha(x)), c\in\Q$$ |
are [[regular iterate|regular]] at the fixpoint $a$. | are [[regular iterate|regular]] at the fixpoint $a$. | ||
Latest revision as of 07:46, 12 November 2025
The principal Abel function (up to an additive constant) of $f$ at fixpoint $a$ is the Abel function of $f$ such that the fractional iterates $\phi_c$ defined by $$\phi_c(x) = \alpha^{-1}(c+\alpha(x)), c\in\Q$$ are regular at the fixpoint $a$.