Hyperbolic-parabolic deformations of rational maps

Abstract We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges unifor...
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Autor*in:	Cui, Guizhen [verfasserIn] Tan, Lei [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2018

Schlagwörter:	rational map geometrically finite hyperbolic parabolic

Übergeordnetes Werk:	Enthalten in: Science in China - Asheville, NC : Science in China Press, 1995, 61(2018), 12 vom: 22. Nov., Seite 2157-2220
Übergeordnetes Werk:	volume:61 ; year:2018 ; number:12 ; day:22 ; month:11 ; pages:2157-2220

Links:	Volltext

DOI / URN:	10.1007/s11425-018-9426-4

Katalog-ID:	SPR019145705

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allfields	10.1007/s11425-018-9426-4 doi (DE-627)SPR019145705 (SPR)s11425-018-9426-4-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Cui, Guizhen verfasserin aut Hyperbolic-parabolic deformations of rational maps 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics. rational map (dpeaa)DE-He213 geometrically finite (dpeaa)DE-He213 hyperbolic (dpeaa)DE-He213 parabolic (dpeaa)DE-He213 Tan, Lei verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 61(2018), 12 vom: 22. Nov., Seite 2157-2220 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:61 year:2018 number:12 day:22 month:11 pages:2157-2220 https://dx.doi.org/10.1007/s11425-018-9426-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 61 2018 12 22 11 2157-2220
spelling	10.1007/s11425-018-9426-4 doi (DE-627)SPR019145705 (SPR)s11425-018-9426-4-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Cui, Guizhen verfasserin aut Hyperbolic-parabolic deformations of rational maps 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics. rational map (dpeaa)DE-He213 geometrically finite (dpeaa)DE-He213 hyperbolic (dpeaa)DE-He213 parabolic (dpeaa)DE-He213 Tan, Lei verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 61(2018), 12 vom: 22. Nov., Seite 2157-2220 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:61 year:2018 number:12 day:22 month:11 pages:2157-2220 https://dx.doi.org/10.1007/s11425-018-9426-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 61 2018 12 22 11 2157-2220
allfields_unstemmed	10.1007/s11425-018-9426-4 doi (DE-627)SPR019145705 (SPR)s11425-018-9426-4-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Cui, Guizhen verfasserin aut Hyperbolic-parabolic deformations of rational maps 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics. rational map (dpeaa)DE-He213 geometrically finite (dpeaa)DE-He213 hyperbolic (dpeaa)DE-He213 parabolic (dpeaa)DE-He213 Tan, Lei verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 61(2018), 12 vom: 22. Nov., Seite 2157-2220 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:61 year:2018 number:12 day:22 month:11 pages:2157-2220 https://dx.doi.org/10.1007/s11425-018-9426-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 61 2018 12 22 11 2157-2220
allfieldsGer	10.1007/s11425-018-9426-4 doi (DE-627)SPR019145705 (SPR)s11425-018-9426-4-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Cui, Guizhen verfasserin aut Hyperbolic-parabolic deformations of rational maps 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics. rational map (dpeaa)DE-He213 geometrically finite (dpeaa)DE-He213 hyperbolic (dpeaa)DE-He213 parabolic (dpeaa)DE-He213 Tan, Lei verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 61(2018), 12 vom: 22. Nov., Seite 2157-2220 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:61 year:2018 number:12 day:22 month:11 pages:2157-2220 https://dx.doi.org/10.1007/s11425-018-9426-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 61 2018 12 22 11 2157-2220
allfieldsSound	10.1007/s11425-018-9426-4 doi (DE-627)SPR019145705 (SPR)s11425-018-9426-4-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Cui, Guizhen verfasserin aut Hyperbolic-parabolic deformations of rational maps 2018 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics. rational map (dpeaa)DE-He213 geometrically finite (dpeaa)DE-He213 hyperbolic (dpeaa)DE-He213 parabolic (dpeaa)DE-He213 Tan, Lei verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 61(2018), 12 vom: 22. Nov., Seite 2157-2220 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:61 year:2018 number:12 day:22 month:11 pages:2157-2220 https://dx.doi.org/10.1007/s11425-018-9426-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 61 2018 12 22 11 2157-2220
language	English
source	Enthalten in Science in China 61(2018), 12 vom: 22. Nov., Seite 2157-2220 volume:61 year:2018 number:12 day:22 month:11 pages:2157-2220
sourceStr	Enthalten in Science in China 61(2018), 12 vom: 22. Nov., Seite 2157-2220 volume:61 year:2018 number:12 day:22 month:11 pages:2157-2220
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	rational map geometrically finite hyperbolic parabolic
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isfreeaccess_bool	false
container_title	Science in China
authorswithroles_txt_mv	Cui, Guizhen @@aut@@ Tan, Lei @@aut@@
publishDateDaySort_date	2018-11-22T00:00:00Z
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author	Cui, Guizhen
spellingShingle	Cui, Guizhen ddc 510 bkl 30.00 bkl 31.00 misc rational map misc geometrically finite misc hyperbolic misc parabolic Hyperbolic-parabolic deformations of rational maps
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topic_title	510 530 520 ASE 30.00 bkl 31.00 bkl Hyperbolic-parabolic deformations of rational maps rational map (dpeaa)DE-He213 geometrically finite (dpeaa)DE-He213 hyperbolic (dpeaa)DE-He213 parabolic (dpeaa)DE-He213
topic	ddc 510 bkl 30.00 bkl 31.00 misc rational map misc geometrically finite misc hyperbolic misc parabolic
topic_unstemmed	ddc 510 bkl 30.00 bkl 31.00 misc rational map misc geometrically finite misc hyperbolic misc parabolic
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title	Hyperbolic-parabolic deformations of rational maps
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title_full	Hyperbolic-parabolic deformations of rational maps
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author_browse	Cui, Guizhen Tan, Lei
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author2-role	verfasserin
title_sort	hyperbolic-parabolic deformations of rational maps
title_auth	Hyperbolic-parabolic deformations of rational maps
abstract	Abstract We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics.
abstractGer	Abstract We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics.
abstract_unstemmed	Abstract We develop a Thurston-like theory to characterize geometrically finite rational maps, and then apply it to study pinching and plumbing deformations of rational maps. We show that under certain conditions the pinching path converges uniformly and the quasiconformal conjugacy converges uniformly to a semi-conjugacy from the original map to the limit. Conversely, every geometrically finite rational map with parabolic points is the landing point of a pinching path for any prescribed plumbing combinatorics.
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title_short	Hyperbolic-parabolic deformations of rational maps
url	https://dx.doi.org/10.1007/s11425-018-9426-4
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doi_str	10.1007/s11425-018-9426-4
up_date	2024-07-04T00:21:39.280Z
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