On the modulispace of attracting dynamics

Carsten Lunde Petersen

On the modulispace of attracting dynamics

Bidragets oversatte titel: Om modulirummet for tiltrækkende dynamiske systemer

Publikation: Konferencebidrag › Konferenceabstrakt til konference › Forskning

Abstrakt

Et tiltrækkende dynamisk system er et triple (f,W,a), hvor W er en åben delmænde af Riemannkuglen, f er en holomorf afbildning af W in i Riemann kuglen og a er et tiltrækkende periodisk punkt for f. Lad B(a) betegne det af a tiltrukne basin. To tiltrækkende dynamiske systemer (f,W,a) og (f',W',a') er i) Konformt eller Möbius konjugerede hvis der findes en Möbiustransformation M med M(W) = W', M(a) = a' og som konjugerer f til f'. eller er ii) hybridt konjugerede hviss der findes en quasi-konform afbildning φ af Riemann kuglen på sig selv, som opfylder φ(W) = W', φ(a) = a' samt konjugerer f til f' og har dbar afledt 0 n.o. uden for B(a). Modulirummet for et tiltrækkende dynamisk system (f,W,a) er rummet af tiltrækkende dynamiske systemer (f',W',a') som er hybridt ekvivalent med (f,W,a). I foredraget diskuterer jeg egenskaberne ved moduli rummet for forskellige tiltrækkende dynamiske systemer.

Originalsprog	Engelsk
Publikationsdato	2005
Status	Udgivet - 2005
Begivenhed	24th Nordic and 1st Franco-Nordic Congress of Mathematicians - Reykjavik, Island Varighed: 6 jan. 2005 → 9 jan. 2005 Konferencens nummer: 24

Konference

Konference	24th Nordic and 1st Franco-Nordic Congress of Mathematicians
Nummer	24
Land	Island
By	Reykjavik
Periode	06/01/2005 → 09/01/2005

Bibliografisk note

http://www.raunvis.hi.is/24NordicCongress/speakers/?s=petersen

Citer dette

Petersen, C. L. (2005). On the modulispace of attracting dynamics. Abstract fra 24th Nordic and 1st Franco-Nordic Congress of Mathematicians, Reykjavik, Island.

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abstract = "An Attracting Dynamics is a triple (f,W,a), where W is an open subset of the R(iemann) S(phere), f is a holomorphic map from W into the RS and a is an attracting periodic point for f. Denote by B(a) the attracted basin of the orbit of a for f. Two attracting dynamics (f,W,a) and (f',W',a') are i) conformally equivalent iif there is a M{\"o}bius transformation M which maps a to a' and which conjugates dynamics. or ii) hybridly equivalent iff there exists a quasi conformal homeomorphism of RS to itself which maps a to a', which conjugates dynamics and with dbar derivative identically zero on the complement of B(a). The moduli space for the attracting dynamics (f,W,a) is the space of attractings dynamics (f,W,a') which are hybridly equivalent to (f,W,a). The talk will discuss properties of moduli spaces of different attracting dynamics.",

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N2 - An Attracting Dynamics is a triple (f,W,a), where W is an open subset of the R(iemann) S(phere), f is a holomorphic map from W into the RS and a is an attracting periodic point for f. Denote by B(a) the attracted basin of the orbit of a for f. Two attracting dynamics (f,W,a) and (f',W',a') are i) conformally equivalent iif there is a Möbius transformation M which maps a to a' and which conjugates dynamics. or ii) hybridly equivalent iff there exists a quasi conformal homeomorphism of RS to itself which maps a to a', which conjugates dynamics and with dbar derivative identically zero on the complement of B(a). The moduli space for the attracting dynamics (f,W,a) is the space of attractings dynamics (f,W,a') which are hybridly equivalent to (f,W,a). The talk will discuss properties of moduli spaces of different attracting dynamics.

AB - An Attracting Dynamics is a triple (f,W,a), where W is an open subset of the R(iemann) S(phere), f is a holomorphic map from W into the RS and a is an attracting periodic point for f. Denote by B(a) the attracted basin of the orbit of a for f. Two attracting dynamics (f,W,a) and (f',W',a') are i) conformally equivalent iif there is a Möbius transformation M which maps a to a' and which conjugates dynamics. or ii) hybridly equivalent iff there exists a quasi conformal homeomorphism of RS to itself which maps a to a', which conjugates dynamics and with dbar derivative identically zero on the complement of B(a). The moduli space for the attracting dynamics (f,W,a) is the space of attractings dynamics (f,W,a') which are hybridly equivalent to (f,W,a). The talk will discuss properties of moduli spaces of different attracting dynamics.

M3 - Conference abstract for conference

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