Dynamics of post-critically finite maps in higher dimension
We study the dynamics of post-critically finite endomorphisms of P^k(C). We prove that post-critically finite endomorphisms are always post-critically finite all the way down under a mild regularity condition on the post-critical set. We study the eigenvalues of periodic points of post-critically fi...
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| creator | Astorg, Matthieu |
| description | We study the dynamics of post-critically finite endomorphisms of P^k(C). We
prove that post-critically finite endomorphisms are always post-critically
finite all the way down under a mild regularity condition on the post-critical
set. We study the eigenvalues of periodic points of post-critically finite
endomorphisms. Then, under a weak transversality condition and assuming
Kobayashi hyperbolicity of the complement of the post-critical set, we prove
that the only possible Fatou components are super-attracting basins, thus
partially extending to any dimension a result of Fornaess-Sibony and Rong
holding in the case k = 2. |
| doi_str_mv | 10.48550/arxiv.1609.02717 |
| format | Article |
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prove that post-critically finite endomorphisms are always post-critically
finite all the way down under a mild regularity condition on the post-critical
set. We study the eigenvalues of periodic points of post-critically finite
endomorphisms. Then, under a weak transversality condition and assuming
Kobayashi hyperbolicity of the complement of the post-critical set, we prove
that the only possible Fatou components are super-attracting basins, thus
partially extending to any dimension a result of Fornaess-Sibony and Rong
holding in the case k = 2.</description><identifier>DOI: 10.48550/arxiv.1609.02717</identifier><language>eng</language><subject>Mathematics - Dynamical Systems</subject><creationdate>2016-09</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1609.02717$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1609.02717$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Astorg, Matthieu</creatorcontrib><title>Dynamics of post-critically finite maps in higher dimension</title><description>We study the dynamics of post-critically finite endomorphisms of P^k(C). We
prove that post-critically finite endomorphisms are always post-critically
finite all the way down under a mild regularity condition on the post-critical
set. We study the eigenvalues of periodic points of post-critically finite
endomorphisms. Then, under a weak transversality condition and assuming
Kobayashi hyperbolicity of the complement of the post-critical set, we prove
that the only possible Fatou components are super-attracting basins, thus
partially extending to any dimension a result of Fornaess-Sibony and Rong
holding in the case k = 2.</description><subject>Mathematics - Dynamical Systems</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzNDOw1DMwMjc052SwdqnMS8zNTC5WyE9TKMgvLtFNLsosyUxOzMmpVEjLzMssSVXITSwoVsjMU8jITM9ILVJIycxNzSvOzM_jYWBNS8wpTuWF0twM8m6uIc4eumBr4guKMnMTiyrjQdbFg60zJqwCAOOCNSY</recordid><startdate>20160909</startdate><enddate>20160909</enddate><creator>Astorg, Matthieu</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20160909</creationdate><title>Dynamics of post-critically finite maps in higher dimension</title><author>Astorg, Matthieu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_1609_027173</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Mathematics - Dynamical Systems</topic><toplevel>online_resources</toplevel><creatorcontrib>Astorg, Matthieu</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Astorg, Matthieu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamics of post-critically finite maps in higher dimension</atitle><date>2016-09-09</date><risdate>2016</risdate><abstract>We study the dynamics of post-critically finite endomorphisms of P^k(C). We
prove that post-critically finite endomorphisms are always post-critically
finite all the way down under a mild regularity condition on the post-critical
set. We study the eigenvalues of periodic points of post-critically finite
endomorphisms. Then, under a weak transversality condition and assuming
Kobayashi hyperbolicity of the complement of the post-critical set, we prove
that the only possible Fatou components are super-attracting basins, thus
partially extending to any dimension a result of Fornaess-Sibony and Rong
holding in the case k = 2.</abstract><doi>10.48550/arxiv.1609.02717</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Dynamical Systems |
| title | Dynamics of post-critically finite maps in higher dimension |
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