74:
53:
84:
150:
22:
287:
Not sure what the comment below means, but there is certainly an error in the section about r=4 case of logistic map being bit-shift under sine square change of variables. The r=4 case of the logistic map then looks like the tent map, not the bit-shift map. It is just as chaotic, but the manners in
260:
Please can you clarify (within the article) your sentence "Equivalently, if we are able to view each iterate of as it actually occurs (as opposed to our simulated values), then we obtain an information flow of one bit per iteration, compared to what we would have known from our simulation." at the
553:
644:
288:
which these two transformations map (0.5,1) to (0,1) are reversed. I don't think these are topologically conjugate. (Disclaimer: I am actually a topologist, but not a dynamicist). -- Denis
324:
What does the colormap in the first image encode? Does the brightness correspond to the number of appearances or the darkness? Is it even accumulative? The caption should be improved.
210:
406:
402:
388:
689:
158:
684:
140:
130:
694:
679:
470:
289:
564:
656:
339:
384:
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
374:
464:
In the derivation to prove that periodic and preperiodic orbits are orbits of rational numbers, the derivation should read
97:
58:
449:
33:
405:
to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
265:. It is not clear what "as it actually occurs" means, and where the "information flow" is flowing from and to.
21:
440:
366:
335:
293:
213:
183:
660:
362:
89:
424:
If you have discovered URLs which were erroneously considered dead by the bot, you can report them with
412:
358:
39:
365:. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit
331:
652:
327:
270:
247:
232:
409:
before doing mass systematic removals. This message is updated dynamically through the template
425:
375:
https://web.archive.org/web/20130212163126/http://www.maths.bristol.ac.uk/~maxcu/Doubling.pdf
310:
432:
106:
73:
52:
391:, "External links modified" talk page sections are no longer generated or monitored by
266:
243:
228:
431:
If you found an error with any archives or the URLs themselves, you can fix them with
673:
378:
227:
Okay, I'll merge the bit shift map article into the dyadic transformation article.
149:
664:
454:
398:
343:
314:
306:
297:
274:
251:
236:
217:
397:. No special action is required regarding these talk page notices, other than
79:
263:
Rate of information loss and sensitive dependence on initial conditions
102:
548:{\displaystyle y\sum _{j=0}^{\infty }2^{-jm}={\frac {y}{1-2^{-m}}}}
639:{\displaystyle y\sum _{j=0}^{\infty }2^{-jm}={\frac {y}{1-2^{m}}}}
15:
148:
369:
for additional information. I made the following changes:
460:
Periodicity via bit shifts rationality of periodic orbits
567:
473:
186:
401:using the archive tool instructions below. Editors
638:
547:
379:http://www.maths.bristol.ac.uk/~maxcu/Doubling.pdf
204:
387:This message was posted before February 2018.
8:
101:, which collaborates on articles related to
19:
650:
357:I have just modified one external link on
325:
47:
627:
611:
596:
586:
575:
566:
533:
517:
502:
492:
481:
472:
305:0.75 -32ieww 10:04PM 11/19/2015 NY time
193:
189:
188:
185:
205:{\displaystyle \mathbb {R} ^{\infty },}
49:
223:Merge bit shift map into this article
7:
157:This article is within the field of
95:This article is within the scope of
38:It is of interest to the following
587:
493:
194:
14:
361:. Please take a moment to review
690:Systems articles in chaos theory
82:
72:
51:
20:
685:Mid-importance Systems articles
135:This article has been rated as
283:Correspondence to logistic map
1:
455:02:20, 27 December 2017 (UTC)
344:00:04, 30 November 2017 (UTC)
315:03:04, 20 November 2015 (UTC)
218:18:14, 2 September 2009 (UTC)
115:Knowledge:WikiProject Systems
695:WikiProject Systems articles
680:Start-Class Systems articles
118:Template:WikiProject Systems
711:
418:(last update: 5 June 2024)
354:Hello fellow Wikipedians,
141:project's importance scale
156:
134:
67:
46:
298:17:15, 2 June 2017 (UTC)
275:10:30, 29 May 2010 (UTC)
252:17:21, 28 May 2010 (UTC)
237:19:05, 27 May 2010 (UTC)
665:16:40, 5 May 2021 (UTC)
350:External links modified
640:
591:
549:
497:
206:
153:
90:Systems science portal
28:This article is rated
641:
571:
550:
477:
359:Dyadic transformation
303:Bit-shift: 0.75-: -->
207:
152:
565:
471:
399:regular verification
184:
389:After February 2018
304:0.5 r=4: 0.75-: -->
261:end of the section
98:WikiProject Systems
636:
545:
443:InternetArchiveBot
394:InternetArchiveBot
202:
154:
34:content assessment
667:
655:comment added by
634:
543:
419:
346:
330:comment added by
180:Hi, what means :
173:
172:
169:
168:
165:
164:
702:
645:
643:
642:
637:
635:
633:
632:
631:
612:
607:
606:
590:
585:
554:
552:
551:
546:
544:
542:
541:
540:
518:
513:
512:
496:
491:
453:
444:
417:
416:
395:
211:
209:
208:
203:
198:
197:
192:
123:
122:
121:Systems articles
119:
116:
113:
92:
87:
86:
85:
76:
69:
68:
63:
55:
48:
31:
25:
24:
16:
710:
709:
705:
704:
703:
701:
700:
699:
670:
669:
649:as it is now.
623:
616:
592:
563:
562:
529:
522:
498:
469:
468:
462:
447:
442:
410:
403:have permission
393:
367:this simple FaQ
352:
322:
320:Image color map
285:
225:
187:
182:
181:
178:
120:
117:
114:
111:
110:
107:systems science
88:
83:
81:
61:
32:on Knowledge's
29:
12:
11:
5:
708:
706:
698:
697:
692:
687:
682:
672:
671:
647:
646:
630:
626:
622:
619:
615:
610:
605:
602:
599:
595:
589:
584:
581:
578:
574:
570:
556:
555:
539:
536:
532:
528:
525:
521:
516:
511:
508:
505:
501:
495:
490:
487:
484:
480:
476:
461:
458:
437:
436:
429:
382:
381:
373:Added archive
351:
348:
321:
318:
302:
284:
281:
280:
279:
278:
277:
255:
254:
224:
221:
201:
196:
191:
177:
174:
171:
170:
167:
166:
163:
162:
155:
145:
144:
137:Mid-importance
133:
127:
126:
124:
94:
93:
77:
65:
64:
62:Mid‑importance
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
707:
696:
693:
691:
688:
686:
683:
681:
678:
677:
675:
668:
666:
662:
658:
654:
628:
624:
620:
617:
613:
608:
603:
600:
597:
593:
582:
579:
576:
572:
568:
561:
560:
559:
537:
534:
530:
526:
523:
519:
514:
509:
506:
503:
499:
488:
485:
482:
478:
474:
467:
466:
465:
459:
457:
456:
451:
446:
445:
434:
430:
427:
423:
422:
421:
414:
408:
404:
400:
396:
390:
385:
380:
376:
372:
371:
370:
368:
364:
360:
355:
349:
347:
345:
341:
337:
333:
329:
319:
317:
316:
312:
308:
300:
299:
295:
291:
290:192.16.204.74
282:
276:
272:
268:
264:
259:
258:
257:
256:
253:
249:
245:
241:
240:
239:
238:
234:
230:
222:
220:
219:
215:
199:
175:
160:
151:
147:
146:
142:
138:
132:
129:
128:
125:
108:
104:
100:
99:
91:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
657:54.37.18.136
651:— Preceding
648:
557:
463:
441:
438:
413:source check
392:
386:
383:
356:
353:
332:Roxanabujack
326:— Preceding
323:
301:
286:
262:
226:
179:
159:Chaos theory
136:
96:
40:WikiProjects
558:instead of
30:Start-class
674:Categories
450:Report bug
433:this tool
426:this tool
267:Gandalf61
244:Duoduoduo
229:Duoduoduo
653:unsigned
439:Cheers.—
340:contribs
328:unsigned
176:Notation
363:my edit
139:on the
112:Systems
103:systems
59:Systems
307:32ieww
242:Done.
36:scale.
661:talk
336:talk
311:talk
294:talk
271:talk
248:talk
233:talk
214:talk
212:-- (
105:and
407:RfC
377:to
131:Mid
676::
663:)
621:−
598:−
588:∞
573:∑
535:−
527:−
504:−
494:∞
479:∑
420:.
415:}}
411:{{
342:)
338:•
313:)
296:)
273:)
250:)
235:)
216:)
195:∞
659:(
629:m
625:2
618:1
614:y
609:=
604:m
601:j
594:2
583:0
580:=
577:j
569:y
538:m
531:2
524:1
520:y
515:=
510:m
507:j
500:2
489:0
486:=
483:j
475:y
452:)
448:(
435:.
428:.
334:(
309:(
292:(
269:(
246:(
231:(
200:,
190:R
161:.
143:.
109:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
