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Parabolic implosion - from discontinuity to renormalization

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Tame and Wild directions<br />

f ε (z) =z + z 2 + ... + ε<br />

0 is parabolic for f 0<br />

with λ 0 =1<br />

Tame direction<br />

safe side<br />

Wild direction<br />

rich side<br />

narrow chance <strong>to</strong> be rich<br />

Continuous change<br />

when restricted <strong>to</strong> tame direction<br />

for example, f(z) =e 2πiα z + ...<br />

α ∈ R

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