Total convergence or general divergence in Small Divisors
classification
🧮 math.DS
nlin.CD
keywords
divisorssmallconvergencedivergencegeneralproblemsarithmeticdifferent
read the original abstract
We study generic holomorphic families of dynamical systems presenting problems of small divisors with fixed arithmetic. We prove that we have convergence for all parameter values or divergence everywhere except for an exceptional set in the potential theory sense. We illustrate this general principle in different problems of small divisors.
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