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Item Details
| Title:
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PROCEEDINGS OF THE SECOND ISAAC CONGRESS
VOLUME 2: THIS PROJECT HAS BEEN EXECUTED WITH GRANT NO. 11-56 FROM THE COMMEMORATIVE ASSOCIATION FOR THE JAPAN WORLD EXPOSITION (1970) |
| By: |
H. Begehr (Editor), Robert P. Gilbert (Editor), Joji Kajiwara (Editor) |
| Format: |
Hardback |
| List price:
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£305.50 |
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| ISBN 10: |
0792365984 |
| ISBN 13: |
9780792365983 |
| Publisher: |
SPRINGER |
| Edition: |
2001 ed. |
| Series: |
International Society for Analysis, Applications and Computation 8 |
| Pages: |
821 |
| Description: |
The emphasis of these 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 text also includes; real and functional analysis, acoustics and computational biology. |
| Synopsis: |
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)). |
| Illustrations: |
XIV, 821 p. |
| Publication: |
Netherlands |
| Imprint: |
Springer |
| Returns: |
Returnable |
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