Entropy of meromorphic maps and dynamics of birational maps:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Soc. Math. de France
2010
|
| Schriftenreihe: | Mémoires de la SMF
122 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | 98 S. |
| ISBN: | 9782856293027 |
Internformat
MARC
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| 100 | 1 | |a Thélin, Henry de |d 1976- |e Verfasser |0 (DE-588)143530216 |4 aut | |
| 245 | 1 | 0 | |a Entropy of meromorphic maps and dynamics of birational maps |c Henry de Thélin ; Gabriel Vigny |
| 264 | 1 | |a Paris |b Soc. Math. de France |c 2010 | |
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Datensatz im Suchindex
| _version_ | 1813056773866651648 |
|---|---|
| adam_text |
CONTENTS
1.
Introduction
. 1
Acknowledgements
. 6
2.
Entropy of meromorphic maps
. 7
2.1.
Push-forward of measures by meromorphic maps
. 7
2.2.
Yomdin's theorem
. 9
2.3.
Proof of Theorem
1 . 11
2.3.1.
Ideas of the proof
. 12
2.3.2.
Proof of Theorem
1 . 13
2.3.3.
Upper bound of vn(Bn{x))
. 14
2.3.4.
Lower bound for the entropy of
μ
. 22
End of the proof of Theorem
1 . 28
3.
Dynamics of
birational
maps of Pk
. 35
3.1.
A family of
birational
maps
. 35
3.2.
Construction of the Green currents
. 43
3.3.
Proof of the genericity (Theorem
3.1.11) . 56
3.4.
The equilibrium measure
. 65
3.4.1.
Construction of the measure
. 65
3.4.2.
Green currents of order
1 <
ç
<
s
. 69
3.4.3.
Mixing, entropy and hyperbolicity of
μ
. 75
A. Super-potentials
. 83
A.I. Definitions and properties of super-potentials
. 83
A.
2.
Additional properties
. 88
Bibliography
. 95
We study the dynamics of meromorphic maps for a compact
Kahler
manifold X. More
precisely, we give a simple criterion that allows us to produce a measure of maximal
entropy. We can apply this result to bound the Lyapunov exponents.
Then, we study the particular case of a family of generic
birational
maps of Pfc
for which we construct the Green currents and the equilibrium measure. We use for
that the theory of super-potentials. We show that the measure is mixing and gives
no mass to pluripolar sets. Using the criterion we get that the measure is of maximal
entropy. It implies finally that the measure is hyperbolic.
On
étudie la dynamique des
applications
méromorphes sur les variétés
kählériennes
compactes. Plus précisément, on donne un critère simple qui permet de produire des
mesures d'entropie maximale. On peut appliquer ce résultat pour borner les exposants
de Lyapounov.
Ensuite, on étudie le cas particulier d'une famille générique d'applications
birationnelles de Pfc pour laquelle on construit les courants de
Green et
la mesure
d'équilibre. On utilise pour cela la théorie des super-potentiels. On montre que la
mesure est mélangeante et qu'elle n'a pas de masse sur les ensembles pluripolaires. En
utilisant le critère on obtient que la mesure est d'entropie maximale. Cela implique
finalement que la mesure est hyperbolique. |
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| id | DE-604.BV037231833 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-16T08:01:19Z |
| institution | BVB |
| isbn | 9782856293027 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021145498 |
| oclc_num | 711826343 |
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| physical | 98 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Soc. Math. de France |
| record_format | marc |
| series | Mémoires de la SMF |
| series2 | Mémoires de la SMF |
| spelling | Thélin, Henry de 1976- Verfasser (DE-588)143530216 aut Entropy of meromorphic maps and dynamics of birational maps Henry de Thélin ; Gabriel Vigny Paris Soc. Math. de France 2010 98 S. txt rdacontent n rdamedia nc rdacarrier Mémoires de la SMF 122 Komplexes System (DE-588)4114261-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Meromorphe Abbildung (DE-588)4778382-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Komplexes System (DE-588)4114261-5 s Meromorphe Abbildung (DE-588)4778382-5 s DE-604 Vigny, Gabriel Verfasser (DE-588)143530283 aut Mémoires de la SMF 122 (DE-604)BV000000921 122 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145498&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145498&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Thélin, Henry de 1976- Vigny, Gabriel Entropy of meromorphic maps and dynamics of birational maps Mémoires de la SMF Komplexes System (DE-588)4114261-5 gnd Dynamisches System (DE-588)4013396-5 gnd Meromorphe Abbildung (DE-588)4778382-5 gnd |
| subject_GND | (DE-588)4114261-5 (DE-588)4013396-5 (DE-588)4778382-5 |
| title | Entropy of meromorphic maps and dynamics of birational maps |
| title_auth | Entropy of meromorphic maps and dynamics of birational maps |
| title_exact_search | Entropy of meromorphic maps and dynamics of birational maps |
| title_full | Entropy of meromorphic maps and dynamics of birational maps Henry de Thélin ; Gabriel Vigny |
| title_fullStr | Entropy of meromorphic maps and dynamics of birational maps Henry de Thélin ; Gabriel Vigny |
| title_full_unstemmed | Entropy of meromorphic maps and dynamics of birational maps Henry de Thélin ; Gabriel Vigny |
| title_short | Entropy of meromorphic maps and dynamics of birational maps |
| title_sort | entropy of meromorphic maps and dynamics of birational maps |
| topic | Komplexes System (DE-588)4114261-5 gnd Dynamisches System (DE-588)4013396-5 gnd Meromorphe Abbildung (DE-588)4778382-5 gnd |
| topic_facet | Komplexes System Dynamisches System Meromorphe Abbildung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145498&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021145498&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000921 |
| work_keys_str_mv | AT thelinhenryde entropyofmeromorphicmapsanddynamicsofbirationalmaps AT vignygabriel entropyofmeromorphicmapsanddynamicsofbirationalmaps |