Periodicities in nonlinear difference equations:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2005
|
| Series: | Advances in discrete mathematics and applications
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 379 S. |
| ISBN: | 0849331560 |
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Record in the Search Index
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| adam_text | ADVANCES IN DISCRETE MATHEMATICS AND APPLICATIONS VOLUME 4 PERIODICITIES
IN NONLINEAR DIFFERENCE EQUATIONS E. A. GROVE G. LADAS CHAPMAN &
HALL/CRC A CRC PRESS COMPANY BOCA RATON LONDON NEW YORK WASHINGTON, D.C.
CONTENTS PREFACE XI ACKNOWLEDGMENTS XIII 1 PRELIMINARIES 1 1.1
INTRODUCTION 1 1.2 DEFINITIONS OF STABILITY AND LINEARIZED STABILITY 1
1.3 SEMI-CYCLE ANALYSIS 8 1.4 FULL LIMITING SEQUENCES 9 1.5 CONVERGENCE
THEOREMS 11 2 EQUATIONS WITH PERIODIC SOLUTIONS 23 2.1 INTRODUCTION 23
2.2 WHAT DO THE FOLLOWING EQUATIONS HAVE IN COMMON? . . . . 23 2.3 WHAT
DO THE FOLLOWING EQUATIONS HAVE IN COMMON? . . . . 27 2.4 LYNESS
EQUATION 28 2.5 TODD S EQUATION 34 2.6 THE GINGERBREADMAN EQUATION 35
2.7 THE GENERALIZED LOZI EQUATION 38 2.8 WHEN IS EVERY SOLUTION OF XN+I
= PERIODIC A + BX + CX A + BX N WITH THE SAME PERIOD? 40 2.9 PERIOD-2
SOLUTIONS OF X N+1 = * P 7 43 A + BX N + CX N .. X 2.9.1 THE CASE C = 0
43 2.9.2 THE CASE C 0 44 2.9.3 EQUATIONS WITH A UNIQUE PRIME
PERIOD-TWO SOLUTION . 45 2.10 THE RICCATI DIFFERENCE EQUATION 47 2.11
SHARKOVSKY S THEOREM 52 2.12 PERIOD 3 IMPLIES CHAOS 53 2.13 OPEN
PROBLEMS AND CONJECTURES 55 3 EQUATIONS WITH EVENTUALLY PERIODIC
SOLUTIONS 61 3.1 INTRODUCTION 61 F 1 A 3.2 THE EQUATION X N +I = MAX
*, 61 I, X N X N -X) 3.3 MAX EQUATIONS WITH PERIODIC COEFFICIENTS 65
VN VLLL 3.4 THE (3A; + 1) CONJECTURE 66 3.5 PERIODICITIES IN THE SPIRIT
OF THE (3A; + 1) CONJECTURE . . . . 67 3.6 OPEN PROBLEMS AND CONJECTURES
70 CONVERGENCE TO PERIODIC SOLUTIONS 75 4.1 INTRODUCTION 75 X N I 4.2 A
TRICHOTOMY RESULT FOR THE EQUATION X N +I = A- 75 X N 4.2.1
PRELIMINARIES 76 4.2.2 ANALYSIS OF THE SEMI-CYCLES OF EQ.(4.1) 78 4.2.3
THE CASE 0 A 1 79 4.2.4 THE CASE A = 1 80 4.2.5 THE CASE A. 1 81
4.3 THE EQUATION X N+1 = 1 + ^ R L 83 X N -2 X N * 1 4.4 THE EQUATION
X N+1 = P N - 84 X N 4.4.1 DECOUPLING THE EVEN AND ODD TERMS 84 4.4.2
LOCAL STABILITY OF EQS.(4.6) AND (4.7) 85 4.4.3 PERIOD-2 SOLUTIONS OF
EQ.(4.5) 88 4.4.4 GLOBAL ASYMPTOTIC STABILITY OF THE PERIOD-2 SOLUTION .
89 4.4.5 EXISTENCE OF UNBOUNDED SOLUTIONS 91 4.4.6 COMPARISON OF LIMITS
92 4.5 THE EQUATION X N+ I = * H * - 1 ^ - ... 93 X N X N -1 XN-K+1 4.6
CONVERGENCE OF SOLUTIONS OF SYSTEMS TO PERIOD-2 SOLUTIONS . 99 4.7 OPEN
PROBLEMS AND CONJECTURES 102 THE EQUATION X N+1 = + ** - *+* + FA -
M M A + XN-2L 5.1 INTRODUCTION AND PRELIMINARIES ILL + 5.2 THE EQUATION
X N +I = + G -(A»+I) N 4 1 + X N -2L 5.2.1 PRELIMINARIES 115 5.2.2
PERIOD-2 SOLUTIONS 118 5.2.3 PERIOD-2D SOLUTIONS 124 5.3 THE EQUATION X
N +I - A + IC -(2FC+I) 125 A + XN-2L 5.3.1 LOCAL STABILITY CHARACTER OF
THE EQUILIBRIUM POINT . . 125 5.3.2 THE CASE A = A = 0 127 5.3.3 THE
CASE 0 A AND 1 A 127 5.3.4 THE CASE 0 A AND 0 A 1 128 5.3.5
THE CASE A = 0 AND A 0 137 5.3.6 THE TRICHOTOMY RESULT FOR EQ.(5.13)
141 5.4 THE EQUATION X N+1 = ** :L - L 141 A + XN-2L IX 5.4.1 ATTRACTING
INTERVALS OF EQ.(5.20) 142 5.4.2 STABILITY CHARACTER OF THE EQUILIBRIUM
POINTS 145 5.4.3 PERIODIC SOLUTIONS OF EQ.(5.20) 153 5.4.4 EXISTENCE OF
UNBOUNDED SOLUTIONS WHEN 7 A + 1 . 153 5.4.5 THE TRICHOTOMY RESULT FOR
EQ.(5.20) 155 5.5 THE REMAINING CASES OF EQ.(5.1) 155 5.5.1 THE CASE 7 =
S = A = 0 155 5.5.2 THE CASE 7 = 0 AND S + A 0 155 5.5.3 THE CASE 7
0 156 5.6 OPEN PROBLEMS AND CONJECTURES 161 6 MAX EQUATIONS WITH
PERIODIC SOLUTIONS 171 6.1 INTRODUCTION 171 6.2 THE MAX EQUATION X N+1 =
^-^*- 171 X N -1 6.2.1 BOUNDEDNESS AND PERSISTENCE OF SOLUTIONS 172
6.2.2 OSCILLATION OF SOLUTIONS 173 6.2.3 PERIODICITY OF SOLUTIONS OF
EQ.(6.2) 178 MAX |A! N , A 6.3 THE MAX EQUATION X N +I = L - ! ^*- 185
X N X N * 1 6.3.1 THE CASE WHERE A IS POSITIVE 186 6.3.2 THE CASE WHERE
A I S NEGATIVE 203 MAX IX 2 , A 6.4 THE MAX EQUATION X N +I = ^-^ *-
205 X N X N *1 6.5 THE MAX EQUATION X N +I * ~^ *- 206 XLXN-L 6.6 THE
MAX EQUATION X^+I = ^^** 208 X N -1 6.7 THE MAX EQUATION X N +I = MAX {
A? A ») 210 X N X N * 1 6.7.1 BOUNDEDNESS AND PERSISTENCE OF
SOLUTIONS OF EQ.(6.21) 210 6.7.2 PERIODICITY 213 6.8 OPEN PROBLEMS AND
CONJECTURES 216 7 MAX EQUATIONS WITH PERIODIC COEFFICIENTS 219 7.1
INTRODUCTION 219 7.2 THE CASE WHERE {A N } IS A PERIOD-2 SEQUENCE 219
7.2.1 THE CASE WHERE 0 AOAX 1 222 7.2.2 THE CASE WHERE A O A X = 1
229 7.2.3 THE CASE WHERE 1 A 0 A T 230 7.3 PERIOD-3 COEFFICIENTS 237
7.3.1 EVENTUALLY PERIODIC SOLUTIONS WITH PERIOD 2 238 7.3.2 EVENTUALLY
PERIODIC SOLUTIONS WITH PERIOD 12 248 7.3.3 UNBOUNDED SOLUTIONS 261
7.3.4 EVENTUALLY PERIODIC SOLUTIONS WITH PERIOD 3 274 7.4 OPEN PROBLEMS
AND CONJECTURES 302 8 EQUATIONS IN THE SPIRIT OF THE (3X+L) CONJECTURE
305 8.1 INTRODUCTION 305 8.2 PRELIMINARIES 306 8.3 BOUNDEDNESS OF
SOLUTIONS 309 8.4 THE EQUATIONS 316 8.4.1 EQ.(L) 316 8.4.2 EQ.(2) 317
8.4.3 EQ.(3) 321 8.4.4 EQ.(4) 329 8.4.5 EQ.(5) 342 8.4.6 EQ.(6) 343
8.4.7 EQ.(7) 345 8.4.8 EQ.(8) 361 8.5 OPEN PROBLEMS AND CONJECTURES 362
REFERENCES 369 INDEX 379
|
| any_adam_object | 1 |
| author | Grove, Edward A. Ladas, Gerasimos E. |
| author_facet | Grove, Edward A. Ladas, Gerasimos E. |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T21:37:43Z |
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| isbn | 0849331560 |
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| physical | XIII, 379 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Chapman & Hall/CRC |
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| series | Advances in discrete mathematics and applications |
| series2 | Advances in discrete mathematics and applications |
| spelling | Grove, Edward A. Verfasser aut Periodicities in nonlinear difference equations E. A. Grove ; G. Ladas Boca Raton [u.a.] Chapman & Hall/CRC 2005 XIII, 379 S. txt rdacontent n rdamedia nc rdacarrier Advances in discrete mathematics and applications 4 Nichtlineare Differenzengleichung (DE-588)4501519-3 gnd rswk-swf Periodizität (DE-588)4248522-8 gnd rswk-swf Nichtlineare Differenzengleichung (DE-588)4501519-3 s Periodizität (DE-588)4248522-8 s DE-604 Ladas, Gerasimos E. Verfasser aut Advances in discrete mathematics and applications 4 (DE-604)BV012406028 4 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017478729&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grove, Edward A. Ladas, Gerasimos E. Periodicities in nonlinear difference equations Advances in discrete mathematics and applications Nichtlineare Differenzengleichung (DE-588)4501519-3 gnd Periodizität (DE-588)4248522-8 gnd |
| subject_GND | (DE-588)4501519-3 (DE-588)4248522-8 |
| title | Periodicities in nonlinear difference equations |
| title_auth | Periodicities in nonlinear difference equations |
| title_exact_search | Periodicities in nonlinear difference equations |
| title_full | Periodicities in nonlinear difference equations E. A. Grove ; G. Ladas |
| title_fullStr | Periodicities in nonlinear difference equations E. A. Grove ; G. Ladas |
| title_full_unstemmed | Periodicities in nonlinear difference equations E. A. Grove ; G. Ladas |
| title_short | Periodicities in nonlinear difference equations |
| title_sort | periodicities in nonlinear difference equations |
| topic | Nichtlineare Differenzengleichung (DE-588)4501519-3 gnd Periodizität (DE-588)4248522-8 gnd |
| topic_facet | Nichtlineare Differenzengleichung Periodizität |
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