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Talk:Tent map

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74: 53: 84: 150: 22: 447: 634:. In this case, the orbit of a point is the set of images of that point under repeated iterations of the tent map. So the orbit of 0 is {0}, whereas the orbit of 1 is {1,0}. Periodic and eventually periodic points have finite orbits; non-periodic points have infinite orbits. 272: 442:{\displaystyle x_{n+1}=\left\{{\begin{matrix}\mu x_{n}&\mathrm {for} ~~x_{n}\leq {\frac {1}{2}}\\\\\mu (1-x_{n})&\mathrm {for} ~~{\frac {1}{2}}\leq x_{n}.\end{matrix}}\right.} 544: 490: 571: 231: 258: 668: 158: 663: 140: 130: 673: 658: 614: 97: 58: 33: 618: 21: 89: 509: 455: 39: 607:
What is an 'orbit'. The article just uses this term without explaining it. 09:37, 15 March 2013 (UTC)
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There really ought to be a picture of the defining function right at the beginning of the article.
627: 203: 497: 236: 106: 73: 52: 635: 593: 574: 652: 149: 493: 191: 79: 573:. However, I have changed the definition in the article to avoid confusion. 185:
In mathematics, the tent map is an iterated function, in the shape of a tent
260:, it has two linear sections which rise to meet at - it looks like a tent. 102: 643: 596: 577: 500: 194: 15: 148: 436: 300: 552: 512: 458: 275: 239: 206: 565: 538: 506:Yes, the function appears to have two values when 484: 441: 252: 225: 180:Need to explain why it's called a "tent map." 8: 101:, which collaborates on articles related to 19: 546:, but the values coincide - they are both 47: 553: 551: 526: 517: 511: 492:, both values apply. Which is correct? ☢ 472: 463: 457: 423: 406: 391: 380: 346: 337: 318: 310: 299: 280: 274: 244: 238: 211: 205: 49: 190:That's not a good-enough explanation? 7: 539:{\displaystyle x_{n}={\frac {1}{2}}} 485:{\displaystyle x_{n}={\frac {1}{2}}} 157:This article is within the field of 95:This article is within the scope of 38:It is of interest to the following 398: 395: 392: 325: 322: 319: 14: 566:{\displaystyle {\frac {\mu }{2}}} 669:Systems articles in chaos theory 82: 72: 51: 20: 664:Mid-importance Systems articles 135:This article has been rated as 386: 367: 1: 597:12:23, 21 December 2006 (UTC) 115:Knowledge:WikiProject Systems 674:WikiProject Systems articles 659:Start-Class Systems articles 578:15:41, 4 February 2006 (UTC) 501:11:49, 4 February 2006 (UTC) 265:Are these equations correct? 195:14:37, 25 October 2005 (UTC) 118:Template:WikiProject Systems 690: 644:12:42, 15 March 2013 (UTC) 141:project's importance scale 156: 134: 67: 46: 226:{\displaystyle x_{n+1}} 567: 540: 486: 443: 254: 227: 153: 90:Systems science portal 28:This article is rated 568: 541: 487: 444: 255: 253:{\displaystyle x_{n}} 228: 152: 632:orbit (group theory) 550: 510: 456: 273: 237: 204: 98:WikiProject Systems 563: 536: 482: 439: 434: 250: 223: 154: 34:content assessment 613:comment added by 561: 534: 480: 414: 405: 403: 354: 332: 330: 173: 172: 169: 168: 165: 164: 681: 628:orbit (dynamics) 622: 572: 570: 569: 564: 562: 554: 545: 543: 542: 537: 535: 527: 522: 521: 491: 489: 488: 483: 481: 473: 468: 467: 448: 446: 445: 440: 438: 435: 428: 427: 415: 407: 404: 402: 401: 385: 384: 355: 347: 342: 341: 331: 329: 328: 315: 314: 291: 290: 259: 257: 256: 251: 249: 248: 232: 230: 229: 224: 222: 221: 123: 122: 121:Systems articles 119: 116: 113: 92: 87: 86: 85: 76: 69: 68: 63: 55: 48: 31: 25: 24: 16: 689: 688: 684: 683: 682: 680: 679: 678: 649: 648: 615:217.156.133.130 608: 605: 586: 548: 547: 513: 508: 507: 459: 454: 453: 433: 432: 419: 389: 376: 361: 360: 357: 356: 333: 316: 306: 295: 276: 271: 270: 267: 240: 235: 234: 207: 202: 201: 178: 120: 117: 114: 111: 110: 107:systems science 88: 83: 81: 61: 32:on Knowledge's 29: 12: 11: 5: 687: 685: 677: 676: 671: 666: 661: 651: 650: 647: 646: 604: 601: 600: 599: 585: 582: 581: 580: 560: 557: 533: 530: 525: 520: 516: 479: 476: 471: 466: 462: 450: 449: 437: 431: 426: 422: 418: 413: 410: 400: 397: 394: 390: 388: 383: 379: 375: 372: 369: 366: 363: 362: 359: 358: 353: 350: 345: 340: 336: 327: 324: 321: 317: 313: 309: 305: 302: 301: 298: 294: 289: 286: 283: 279: 266: 263: 262: 261: 247: 243: 220: 217: 214: 210: 188: 187: 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: 686: 675: 672: 670: 667: 665: 662: 660: 657: 656: 654: 645: 641: 637: 633: 629: 625: 624: 623: 620: 616: 612: 602: 598: 595: 591: 590: 589: 583: 579: 576: 558: 555: 531: 528: 523: 518: 514: 505: 504: 503: 502: 499: 495: 477: 474: 469: 464: 460: 429: 424: 420: 416: 411: 408: 381: 377: 373: 370: 364: 351: 348: 343: 338: 334: 311: 307: 303: 296: 292: 287: 284: 281: 277: 269: 268: 264: 245: 241: 218: 215: 212: 208: 199: 198: 197: 196: 193: 186: 183: 182: 181: 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: 609:— Preceding 606: 587: 451: 200:If you plot 189: 184: 179: 159:Chaos theory 136: 96: 40:WikiProjects 30:Start-class 653:Categories 636:Gandalf61 594:Gandalf61 575:Gandalf61 611:unsigned 233:versus 139:on the 112:Systems 103:systems 59:Systems 603:Orbit? 592:Done. 36:scale. 494:Ҡieff 192:linas 640:talk 630:and 626:See 619:talk 584:Plot 176:Name 105:and 452:If 131:Mid 655:: 642:) 621:) 556:μ 417:≤ 374:− 365:μ 344:≤ 304:μ 638:( 617:( 559:2 532:2 529:1 524:= 519:n 515:x 498:↯ 496:⌇ 478:2 475:1 470:= 465:n 461:x 430:. 425:n 421:x 412:2 409:1 399:r 396:o 393:f 387:) 382:n 378:x 371:1 368:( 352:2 349:1 339:n 335:x 326:r 323:o 320:f 312:n 308:x 297:{ 293:= 288:1 285:+ 282:n 278:x 246:n 242:x 219:1 216:+ 213:n 209:x 161:. 143:. 109:. 42::

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Chaos theory
linas
14:37, 25 October 2005 (UTC)
Ҡieff

11:49, 4 February 2006 (UTC)
Gandalf61
15:41, 4 February 2006 (UTC)
Gandalf61
12:23, 21 December 2006 (UTC)
unsigned
217.156.133.130
talk
orbit (dynamics)
orbit (group theory)
Gandalf61
talk

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