Computability of Julia sets:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
2009
|
| Series: | Algorithms and computation in mathematics
23 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017169280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverz. S. 146 - 148 |
| Physical Description: | XIII, 151 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783540685463 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035365299 | ||
| 003 | DE-604 | ||
| 005 | 20191114 | ||
| 007 | t| | ||
| 008 | 090312s2009 gw ad|| |||| 00||| eng d | ||
| 015 | |a 08,N21,0613 |2 dnb | ||
| 015 | |a 09,A05,1062 |2 dnb | ||
| 016 | 7 | |a 988539373 |2 DE-101 | |
| 020 | |a 9783540685463 |c Pp. : EUR 64.15 (freier Pr.), sfr 99.50 (freier Pr.) |9 978-3-540-68546-3 | ||
| 024 | 3 | |a 9783540685463 | |
| 028 | 5 | 2 | |a 12228874 |
| 035 | |a (OCoLC)288984413 | ||
| 035 | |a (DE-599)DNB988539373 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-355 |a DE-703 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA614.86 | |
| 082 | 0 | |a 511.32 |2 22/ger | |
| 082 | 0 | |a 514.7420285 |2 22 | |
| 084 | |a ST 134 |0 (DE-625)143590: |2 rvk | ||
| 084 | |a ST 130 |0 (DE-625)143588: |2 rvk | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Braverman, Mark |e Verfasser |0 (DE-588)13686094X |4 aut | |
| 245 | 1 | 0 | |a Computability of Julia sets |c Mark Braverman ; Michael Yampolsky |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2009 | |
| 300 | |a XIII, 151 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Algorithms and computation in mathematics |v 23 | |
| 500 | |a Literaturverz. S. 146 - 148 | ||
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Julia sets |x Data processing | |
| 650 | 0 | 7 | |a Berechenbarkeit |0 (DE-588)4138368-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Julia-Menge |0 (DE-588)4431306-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Julia-Menge |0 (DE-588)4431306-8 |D s |
| 689 | 0 | 1 | |a Berechenbarkeit |0 (DE-588)4138368-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Yampolsky, Michael |d 1972- |e Verfasser |0 (DE-588)136860982 |4 aut | |
| 830 | 0 | |a Algorithms and computation in mathematics |v 23 |w (DE-604)BV011131286 |9 23 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017169280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-017169280 | |
Record in the Search Index
| _version_ | 1819286493716283392 |
|---|---|
| adam_text | Contents
Introduction
to Computability
................................... 1
1.1
Discrete computability and complexity
......................... 1
1.2
Computability and complexity of real numbers and functions
...... 5
1.3
Computability and complexity of subsets of M.k
.................. 11
1.4
Weakly computable sets
..................................... 14
1.5
Set-valued functions and uniformity
........................... 17
Dynamics of Rational Mappings
................................. 21
2.1
General facts about Riemann surfaces and the hyperbolic metric
... 21
2.2
Julia sets of rational mappings
................................ 27
First Examples
................................................. 37
3.1
A case study: hyperbolic Julia sets
............................ 37
3.2
Maps with parabolic orbits
................................... 49
3.3
Computing Julia sets with parabolic orbits efficiently
............. 53
3.4
Lack of uniform computability of Julia sets
..................... 60
Positive Results
................................................ 65
4.1
Computability of filled Julia sets
.............................. 65
4.2
Julia sets without rotation domains
............................ 69
4.3
Computable Julia sets of
Siegel
quadratics
...................... 70
4.4
Robust computability
....................................... 75
Negative Results
............................................... 81
5.1 Siegel
disks and Cremer points
............................... 81
5.2
Non-computable Julia sets
................................... 90
5.3
The complexity of Julia sets
..................................103
5.4
Proofs of the main technical lemmas
...........................107
5.5
Number theory and computability
.............................
Ill
5.6
Quadratics with non-computable Julia sets are rare
...............113
xii Contents
6 Computability vs
Topology
......................................119
6.1
How can the boundary of a computable set be non-computable?
___119
6.2
Locally connected quadratic Julia sets
.........................120
6.3
Local connectedness versus computability of Jg
.................127
6.4
Non-computable locally connected Julia sets
....................136
References
.....................................................146
Index
.............................................................149
|
| any_adam_object | 1 |
| author | Braverman, Mark Yampolsky, Michael 1972- |
| author_GND | (DE-588)13686094X (DE-588)136860982 |
| author_facet | Braverman, Mark Yampolsky, Michael 1972- |
| author_role | aut aut |
| author_sort | Braverman, Mark |
| author_variant | m b mb m y my |
| building | Verbundindex |
| bvnumber | BV035365299 |
| callnumber-first | Q - Science |
| callnumber-label | QA614 |
| callnumber-raw | QA614.86 |
| callnumber-search | QA614.86 |
| callnumber-sort | QA 3614.86 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | ST 134 ST 130 |
| ctrlnum | (OCoLC)288984413 (DE-599)DNB988539373 |
| dewey-full | 511.32 514.7420285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics 514 - Topology |
| dewey-raw | 511.32 514.7420285 |
| dewey-search | 511.32 514.7420285 |
| dewey-sort | 3511.32 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02085nam a2200541 cb4500</leader><controlfield tag="001">BV035365299</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20191114 </controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">090312s2009 gw ad|| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">08,N21,0613</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">09,A05,1062</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">988539373</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783540685463</subfield><subfield code="c">Pp. : EUR 64.15 (freier Pr.), sfr 99.50 (freier Pr.)</subfield><subfield code="9">978-3-540-68546-3</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9783540685463</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">12228874</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)288984413</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB988539373</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA614.86</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.32</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">514.7420285</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 134</subfield><subfield code="0">(DE-625)143590:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 130</subfield><subfield code="0">(DE-625)143588:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Braverman, Mark</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)13686094X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Computability of Julia sets</subfield><subfield code="c">Mark Braverman ; Michael Yampolsky</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ; Heidelberg</subfield><subfield code="b">Springer</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 151 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield><subfield code="c">24 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Algorithms and computation in mathematics</subfield><subfield code="v">23</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 146 - 148</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Julia sets</subfield><subfield code="x">Data processing</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Berechenbarkeit</subfield><subfield code="0">(DE-588)4138368-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Julia-Menge</subfield><subfield code="0">(DE-588)4431306-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Julia-Menge</subfield><subfield code="0">(DE-588)4431306-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Berechenbarkeit</subfield><subfield code="0">(DE-588)4138368-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yampolsky, Michael</subfield><subfield code="d">1972-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)136860982</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Algorithms and computation in mathematics</subfield><subfield code="v">23</subfield><subfield code="w">(DE-604)BV011131286</subfield><subfield code="9">23</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017169280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-017169280</subfield></datafield></record></collection> |
| id | DE-604.BV035365299 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:29:26Z |
| institution | BVB |
| isbn | 9783540685463 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017169280 |
| oclc_num | 288984413 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-11 DE-188 |
| physical | XIII, 151 S. Ill., graph. Darst. 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Algorithms and computation in mathematics |
| series2 | Algorithms and computation in mathematics |
| spellingShingle | Braverman, Mark Yampolsky, Michael 1972- Computability of Julia sets Algorithms and computation in mathematics Datenverarbeitung Julia sets Data processing Berechenbarkeit (DE-588)4138368-0 gnd Julia-Menge (DE-588)4431306-8 gnd |
| subject_GND | (DE-588)4138368-0 (DE-588)4431306-8 |
| title | Computability of Julia sets |
| title_auth | Computability of Julia sets |
| title_exact_search | Computability of Julia sets |
| title_full | Computability of Julia sets Mark Braverman ; Michael Yampolsky |
| title_fullStr | Computability of Julia sets Mark Braverman ; Michael Yampolsky |
| title_full_unstemmed | Computability of Julia sets Mark Braverman ; Michael Yampolsky |
| title_short | Computability of Julia sets |
| title_sort | computability of julia sets |
| topic | Datenverarbeitung Julia sets Data processing Berechenbarkeit (DE-588)4138368-0 gnd Julia-Menge (DE-588)4431306-8 gnd |
| topic_facet | Datenverarbeitung Julia sets Data processing Berechenbarkeit Julia-Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017169280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011131286 |
| work_keys_str_mv | AT bravermanmark computabilityofjuliasets AT yampolskymichael computabilityofjuliasets |