Nonlocal bifurcations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Soc.
1999
|
| Schriftenreihe: | Mathematical surveys and monographs
66 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 286 S. graph. Darst. |
| ISBN: | 0821804979 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV014601192 | ||
| 003 | DE-604 | ||
| 005 | 20230914 | ||
| 007 | t | ||
| 008 | 020731s1999 d||| |||| 00||| eng d | ||
| 020 | |a 0821804979 |9 0-8218-0497-9 | ||
| 035 | |a (OCoLC)472297758 | ||
| 035 | |a (DE-599)BVBBV014601192 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-188 | ||
| 050 | 0 | |a QA380 | |
| 082 | 0 | |a 515 |2 21 | |
| 084 | |a SK 520 |0 (DE-625)143244: |2 rvk | ||
| 100 | 1 | |a Ilʹjašenko, Julij S. |d 1943- |e Verfasser |0 (DE-588)134211898 |4 aut | |
| 245 | 1 | 0 | |a Nonlocal bifurcations |c Yu. Ilyashenko ; Weigu Li |
| 264 | 1 | |a Providence, RI |b American Mathematical Soc. |c 1999 | |
| 300 | |a XIII, 286 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v 66 | |
| 650 | 4 | |a Bifurcation theory | |
| 650 | 0 | 7 | |a Verzweigung |g Mathematik |0 (DE-588)4078889-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Verzweigung |g Mathematik |0 (DE-588)4078889-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Li, Weigu |e Verfasser |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1293-7 |
| 830 | 0 | |a Mathematical surveys and monographs |v 66 |w (DE-604)BV000018014 |9 66 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009924714&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-009924714 | ||
Datensatz im Suchindex
| _version_ | 1804129377177305088 |
|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Introduction 1
§1. Structural stability and Morse Smale systems 1
§2. Equivalence and local bifurcations in generic one parameter fami¬
lies 10
§3. Homoclinic trajectories of nonhyperbolic singular points 17
§4. Homoclinic trajectories of nonhyperbolic cycles 19
§5. Homoclinic loops of hyperbolic fixed points and other contours 22
§6. Summary of results 26
Chapter 2. Preliminaries 31
§1. Prevalence 31
§2. Attractors, their dimensions and projections 34
§3. Smale horseshoe for high school students 48
§4. Some results in hyperbolic theory 57
§5. Normal forms for local families 64
Chapter 3. Bifurcations in the Plane 69
§1. Bifurcations of homoclinic loops of planar saddles 69
§2. Homoclinic orbit of a saddlenode 73
§3. Semistable cycles breaking saddle connections 77
Chapter 4. Homoclinic Orbits of Nonhyperbolic Singular Points 83
§1. Homoclinic orbit of a saddlenode: the case of a nodal hyperbolic
part 83
§2. Lemma on the hyperbolicity of the product of linear maps 87
§3. Homoclinic orbit of a saddlenode: the case of a saddle hyperbolic
part 93
§4. Several homoclinic orbits of a saddlenode 102
§5. Birkhoff Smale theorem 104
Chapter 5. Homoclinic Tori and Klein Bottles of Nonhyperbolic Periodic
Orbits: Noncritical Case 109
§1. The topological and smooth structure of the union of homoclinic
orbits 109
§2. Persistence of noncritical homoclinic tori and Klein bottles 114
§3. The rotation number as a function of the parameter in the family
of diffeomorphisms of the circle 120
vii
viii CONTENTS
§4. Bifurcations on a noncritical homoclinic torus of a generic saddle
node family 127
§5. The blue sky catastrophe on the Klein bottle 131
§6. Generalized Smale horseshoe existence theorem 138
§7. Several noncritical homoclinic tori or Klein bottles of a nonhyper
bolic cycle 142
§8. Generation of a strange attractor via the bifurcation of a twisted
homoclinic surface 153
Chapter 6. Homoclinic Torus of a Nonhyperbolic Periodic Orbit: Semicrit
ical Case 159
§1. Theorem on the generation of a strange attractor 159
§2. Lemmas on limit maps, density and volume contraction 169
§3. Rotation sets and periodic points of circle endomorphisms 170
§4. Homoclinic orbits of circle endomorphisms 174
Chapter 7. Bifurcations of Homoclinic Trajectories of Hyperbolic Saddles 181
§1. The homoclinic trajectory of a hyperbolic saddle with three real
eigenvalues in R3 181
§2. The homoclinic trajectory of a hyperbolic saddle with two complex
eigenvalues in K3 191
§3. Homoclinic orbits of hyperbolic saddles in high dimensional spaces 200
Chapter 8. Elements of Hyperbolic Theory 211
§1. Hyperbolic sets and their properties 211
§2. Introduction to symbolic dynamics 213
§3. Hyperbolic fixed point theorem 215
§4. Sufficient conditions for the existence of a Smale horseshoe 223
§5. The generalized Smale horseshoe 227
Chapter 9. Normal Forms for Local Families: Hyperbolic Case 235
§1. Main results and their reduction to the Belitskii Samovol theorem 235
§2. Introduction to Frobenius theory and the homotopy method 239
§3. Belitskii Samovol theorem for vector fields 244
§4. Belitskii Samovol theorem for maps 250
Chapter 10. Normal Forms for Unfoldings of Saddlenodes 253
§1. Takens theorem on the smooth saddle suspension 253
§2. Unfoldings of saddlenodes 260
§3. Takens smooth saddle suspension theorem for maps 264
§4. Partial embedding theorem for saddlenode families of maps 268
Bibliography 281
|
| any_adam_object | 1 |
| author | Ilʹjašenko, Julij S. 1943- Li, Weigu |
| author_GND | (DE-588)134211898 |
| author_facet | Ilʹjašenko, Julij S. 1943- Li, Weigu |
| author_role | aut aut |
| author_sort | Ilʹjašenko, Julij S. 1943- |
| author_variant | j s i js jsi w l wl |
| building | Verbundindex |
| bvnumber | BV014601192 |
| callnumber-first | Q - Science |
| callnumber-label | QA380 |
| callnumber-raw | QA380 |
| callnumber-search | QA380 |
| callnumber-sort | QA 3380 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 |
| ctrlnum | (OCoLC)472297758 (DE-599)BVBBV014601192 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01543nam a2200397 cb4500</leader><controlfield tag="001">BV014601192</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230914 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">020731s1999 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821804979</subfield><subfield code="9">0-8218-0497-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)472297758</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV014601192</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA380</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 520</subfield><subfield code="0">(DE-625)143244:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ilʹjašenko, Julij S.</subfield><subfield code="d">1943-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)134211898</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonlocal bifurcations</subfield><subfield code="c">Yu. Ilyashenko ; Weigu Li</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, RI</subfield><subfield code="b">American Mathematical Soc.</subfield><subfield code="c">1999</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 286 S.</subfield><subfield code="b">graph. Darst.</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">Mathematical surveys and monographs</subfield><subfield code="v">66</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bifurcation theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Verzweigung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4078889-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Verzweigung</subfield><subfield code="g">Mathematik</subfield><subfield code="0">(DE-588)4078889-1</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">Li, Weigu</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-1293-7</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Mathematical surveys and monographs</subfield><subfield code="v">66</subfield><subfield code="w">(DE-604)BV000018014</subfield><subfield code="9">66</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</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=009924714&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-009924714</subfield></datafield></record></collection> |
| id | DE-604.BV014601192 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:10Z |
| institution | BVB |
| isbn | 0821804979 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009924714 |
| oclc_num | 472297758 |
| open_access_boolean | |
| owner | DE-384 DE-188 |
| owner_facet | DE-384 DE-188 |
| physical | XIII, 286 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | American Mathematical Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Ilʹjašenko, Julij S. 1943- Verfasser (DE-588)134211898 aut Nonlocal bifurcations Yu. Ilyashenko ; Weigu Li Providence, RI American Mathematical Soc. 1999 XIII, 286 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 66 Bifurcation theory Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s DE-604 Li, Weigu Verfasser aut Erscheint auch als Online-Ausgabe 978-1-4704-1293-7 Mathematical surveys and monographs 66 (DE-604)BV000018014 66 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009924714&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ilʹjašenko, Julij S. 1943- Li, Weigu Nonlocal bifurcations Mathematical surveys and monographs Bifurcation theory Verzweigung Mathematik (DE-588)4078889-1 gnd |
| subject_GND | (DE-588)4078889-1 |
| title | Nonlocal bifurcations |
| title_auth | Nonlocal bifurcations |
| title_exact_search | Nonlocal bifurcations |
| title_full | Nonlocal bifurcations Yu. Ilyashenko ; Weigu Li |
| title_fullStr | Nonlocal bifurcations Yu. Ilyashenko ; Weigu Li |
| title_full_unstemmed | Nonlocal bifurcations Yu. Ilyashenko ; Weigu Li |
| title_short | Nonlocal bifurcations |
| title_sort | nonlocal bifurcations |
| topic | Bifurcation theory Verzweigung Mathematik (DE-588)4078889-1 gnd |
| topic_facet | Bifurcation theory Verzweigung Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009924714&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT ilʹjasenkojulijs nonlocalbifurcations AT liweigu nonlocalbifurcations |