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)
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Boston, MA
Springer US
2000
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| Schriftenreihe: | International Society for Analysis, Applications and Computation
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| Beschreibung: | 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)) |
| Beschreibung: | 1 Online-Ressource (XIV, 821 p) |
| ISBN: | 9781461302711 9781461379713 |
| ISSN: | 1388-4271 |
| DOI: | 10.1007/978-1-4613-0271-1 |
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| 245 | 1 | 0 | |a Proceedings of the Second ISAAC Congress |b Volume 2: This project has been executed with Grant No. 11–56 from the Commemorative Association for the Japan World Exposition (1970) |c edited by Heinrich G. W. Begehr, Robert P. Gilbert, Joji Kajiwara |
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| 490 | 0 | |a International Society for Analysis, Applications and Computation |v 8 |x 1388-4271 | |
| 500 | |a 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)) | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Functional analysis | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Integral equations | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Integral Equations | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a Functions of a Complex Variable | |
| 650 | 4 | |a Several Complex Variables and Analytic Spaces | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a Gilbert, Robert P. |e Sonstige |4 oth | |
| 700 | 1 | |a Kajiwara, Joji |e Sonstige |4 oth | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Begehr, Heinrich G. W. |
| author_facet | Begehr, Heinrich G. W. |
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| author_sort | Begehr, Heinrich G. W. |
| author_variant | h g w b hgw hgwb |
| building | Verbundindex |
| bvnumber | BV042420586 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)905369113 (DE-599)BVBBV042420586 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-0271-1 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461302711 9781461379713 |
| issn | 1388-4271 |
| language | English |
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| spelling | Begehr, Heinrich G. W. Verfasser aut 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) edited by Heinrich G. W. Begehr, Robert P. Gilbert, Joji Kajiwara Boston, MA Springer US 2000 1 Online-Ressource (XIV, 821 p) txt rdacontent c rdamedia cr rdacarrier International Society for Analysis, Applications and Computation 8 1388-4271 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)) Mathematics Functional analysis Functions of complex variables Integral equations Differential equations, partial Partial Differential Equations Integral Equations Functional Analysis Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematik Gilbert, Robert P. Sonstige oth Kajiwara, Joji Sonstige oth https://doi.org/10.1007/978-1-4613-0271-1 Verlag Volltext |
| spellingShingle | Begehr, Heinrich G. W. 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) Mathematics Functional analysis Functions of complex variables Integral equations Differential equations, partial Partial Differential Equations Integral Equations Functional Analysis Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematik |
| title | 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) |
| title_auth | 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) |
| title_exact_search | 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) |
| title_full | 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) edited by Heinrich G. W. Begehr, Robert P. Gilbert, Joji Kajiwara |
| title_fullStr | 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) edited by Heinrich G. W. Begehr, Robert P. Gilbert, Joji Kajiwara |
| title_full_unstemmed | 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) edited by Heinrich G. W. Begehr, Robert P. Gilbert, Joji Kajiwara |
| title_short | Proceedings of the Second ISAAC Congress |
| title_sort | 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 |
| title_sub | Volume 2: This project has been executed with Grant No. 11–56 from the Commemorative Association for the Japan World Exposition (1970) |
| topic | Mathematics Functional analysis Functions of complex variables Integral equations Differential equations, partial Partial Differential Equations Integral Equations Functional Analysis Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematik |
| topic_facet | Mathematics Functional analysis Functions of complex variables Integral equations Differential equations, partial Partial Differential Equations Integral Equations Functional Analysis Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematik |
| url | https://doi.org/10.1007/978-1-4613-0271-1 |
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