SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS
We study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations, in two settings: (1) rational curves that ar...
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2013-01-01
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| Series: | Forum of Mathematics, Pi |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050508613000024/type/journal_article |
| _version_ | 1827994957578764288 |
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| author | MATTHEW BAKER LAURA DE MARCO |
| author_facet | MATTHEW BAKER LAURA DE MARCO |
| author_sort | MATTHEW BAKER |
| collection | DOAJ |
| description | We study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations, in two settings: (1) rational curves that are polynomially parameterized; and (2) cubic polynomials defined by a given fixed point multiplier. We offer a conjecture on the general form of algebraic subvarieties in the moduli space of rational maps on ${ \mathbb{P} }^{1} $ containing a Zariski-dense subset of postcritically finite maps. |
| first_indexed | 2024-04-10T04:49:03Z |
| format | Article |
| id | doaj.art-22a52d92f60e4a5c9cfc9515e37b6bbf |
| institution | Directory Open Access Journal |
| issn | 2050-5086 |
| language | English |
| last_indexed | 2024-04-10T04:49:03Z |
| publishDate | 2013-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj.art-22a52d92f60e4a5c9cfc9515e37b6bbf2023-03-09T12:34:16ZengCambridge University PressForum of Mathematics, Pi2050-50862013-01-01110.1017/fmp.2013.2SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALSMATTHEW BAKER0LAURA DE MARCO1Georgia Institute of Technology, Mathematics Atlanta, GA, United StatesUniversity of Illinois at Chicago, Mathematics Chicago, IL, United StatesWe study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations, in two settings: (1) rational curves that are polynomially parameterized; and (2) cubic polynomials defined by a given fixed point multiplier. We offer a conjecture on the general form of algebraic subvarieties in the moduli space of rational maps on ${ \mathbb{P} }^{1} $ containing a Zariski-dense subset of postcritically finite maps.https://www.cambridge.org/core/product/identifier/S2050508613000024/type/journal_article37F45 (primary)11G5030C10 (secondary) |
| spellingShingle | MATTHEW BAKER LAURA DE MARCO SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS Forum of Mathematics, Pi 37F45 (primary) 11G50 30C10 (secondary) |
| title | SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS |
| title_full | SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS |
| title_fullStr | SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS |
| title_full_unstemmed | SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS |
| title_short | SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS |
| title_sort | special curves and postcritically finite polynomials |
| topic | 37F45 (primary) 11G50 30C10 (secondary) |
| url | https://www.cambridge.org/core/product/identifier/S2050508613000024/type/journal_article |
| work_keys_str_mv | AT matthewbaker specialcurvesandpostcriticallyfinitepolynomials AT laurademarco specialcurvesandpostcriticallyfinitepolynomials |