Proceedings of the Second ISAAC Congress: Volume 2: This project has been executed with Grant No. 11-56 from the Commemorative Association for the ... Analysis, Applications and Computation, 8) - Softcover

Softcover

ISBN 10: 1461379717 ISBN 13: 9781461379713

Verlag: Springer, 2011

Inhaltsangabe

Let 8 be a Riemann surface of analytically finite type (9, n) with 29 - 2+n> O. Take two pointsP1, P2 E 8, and set 8 ,1>2= 8 \ {P1' P2}. Let PI Homeo+(8;P1,P2) be the group of all orientation preserving homeomor- phismsw: 8 -+ 8 fixingP1, P2 and isotopic to the identity on 8. Denote byHomeot(8;Pb P2) the set of all elements ofHomeo+(8;P1, P2) iso- topic to the identity on 8 ,P2' ThenHomeot(8;P1,P2) is a normal sub- pl group ofHomeo+(8;P1,P2). We setIsot(8;P1,P2) =Homeo+(8;P1,P2)/ Homeot(8;p1, P2). The purpose of this note is to announce a result on the Nielsen- Thurston-Bers type classification of an element [w] ofIsot+(8;P1,P2). We give a necessary and sufficient condition for thetypeto be hyperbolic. The condition is described in terms of properties of the pure braid [b ] w induced by [w]. Proofs will appear elsewhere. The problem considered in this note and the form ofthe solution are suggested by Kra's beautiful theorem in [6], where he treats self-maps of Riemann surfaces with one specified point. 2 TheclassificationduetoBers Let us recall the classification of elements of the mapping class group due to Bers (see Bers [1]). LetT(R) be the Teichmiiller space of a Riemann surfaceR, andMod(R) be the Teichmtiller modular group of R. Note that an orientation preserving homeomorphism w: R -+ R induces canonically an element (w) EMod(R). Denote by&.r(R)(*,.) the Teichmiiller distance onT(R). For an elementXEMod(R), we define a(x)= inf &.r(R)(r,x(r)).

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Reseña del editor

The emphasis of the two volumes is on complex analysis with classical topics such as value distribution, and modern topics such as complex dynamics, both in one and several complex variables; the application of complex analysis to partial differential equations and integral equations and its generalization to quaternionic and Clifford analysis; new results from real and functional analysis, numerical and computational mathematics; and areas in applied mathematics such as acoustics and computational biology. Audience: Researchers, especially those working in real and complex analysis, in numerical analysis, and in mathematical physics.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2011
• Sprache: Englisch
• ISBN 10: 1461379717
• ISBN 13: 9781461379713
• Einband: Tapa blanda
• Anzahl der Seiten: 840
• Herausgeber: Begehr Heinrich G.W., Gilbert R.P., Kajiwara Joji
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Deutschland