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Satellite renormalisations and small divisors
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TIFR International Colloquium 2024
Davoud Cheraghi (Imperial College)
Presence of renormalisation structures is a main obstacle in the study of nonlinear dynamics. In dimension one, renormalisation structures come in two flavours, primitive type and satellite type. While the renormalisation of primitive type has been successfully studied in the last four decades, the renormalisation of satellite type remained mysterious until recently. In this talk we review the primitive renormalisations and present new developments in the study of satellite renormalisations. The connections to the problems of small divisors and the local connectivity of the Mandelbrot set will be discussed.
Davoud Cheraghi (Imperial College)
Presence of renormalisation structures is a main obstacle in the study of nonlinear dynamics. In dimension one, renormalisation structures come in two flavours, primitive type and satellite type. While the renormalisation of primitive type has been successfully studied in the last four decades, the renormalisation of satellite type remained mysterious until recently. In this talk we review the primitive renormalisations and present new developments in the study of satellite renormalisations. The connections to the problems of small divisors and the local connectivity of the Mandelbrot set will be discussed.