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 $\ph$ defined by |
$$\ph(x) = \alpha^{-1}(c+\alpha(x)), c\in\Q$$ | $$\ph(x) = \alpha^{-1}(c+\alpha(x)), c\in\Q$$ | ||
are [[regular iterate|regular]] at the fixpoint $a$. | are [[regular iterate|regular]] at the fixpoint $a$. | ||
Revision as of 13:20, 7 June 2011
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 $\ph$ defined by $$\ph(x) = \alpha^{-1}(c+\alpha(x)), c\in\Q$$ are regular at the fixpoint $a$.