function T=Arnoldp(N);
% 计算Arnold变换的周期
C=[1,1;1,2];
[x,y]=meshgrid(1:N);
P0=[x(:)';y(:)'];
P1=[x(:)';y(:)'];
for k=1:N^2/2+1;
P1=rem(C*P1-1,N)+1;
s=max(max(abs(P1-P0)));
if s<1;
T=k;
break;
end
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
调用下面一段程序可以计算相应的周期T:
for k=1:1000;
T=Arnoldp(k);
disp(['(',num2str(k),',',num2str(T),')'])
end
N在1000以内的周期T如下所列:
(N,T)
(1,1)
(2,3)
(3,4)
(4,3)
(5,10)
(6,12)
(7,8)
(8,6)
(9,12)
(10,30)
(11,5)
(12,12)
(13,14)
(14,24)
(15,20)
(16,12)
(17,18)
(18,12)
(19,9)
(20,30)
(21,8)
(22,15)
(23,24)
(24,12)
(25,50)
(26,42)
(27,36)
(28,24)
(29,7)
(30,60)
(31,15)
(32,24)
(33,20)
(34,18)
(35,40)
(36,12)
(37,38)
(38,9)
(39,28)
(40,30)
(41,20)
(42,24)
(43,44)
(44,15)
(45,60)
(46,24)
(47,16)
(48,12)
(49,56)
(50,150)
(51,36)
(52,42)
(53,54)
(54,36)
(55,10)
(56,24)
(57,36)
(58,21)
(59,29)
(60,60)
(61,30)
(62,15)
(63,24)
(64,48)
(65,70)
(66,60)
(67,68)
(68,18)
(69,24)
(70,120)
(71,35)
(72,12)
(73,74)
(74,114)
(75,100)
(76,9)
(77,40)
(78,84)
(79,39)
(80,60)
(81,108)
(82,60)
(83,84)
(84,24)
(85,90)
(86,132)
(87,28)
(88,30)
(89,22)
(90,60)
(91,56)
(92,24)
(93,60)
(94,48)
(95,90)
(96,24)
(97,98)
(98,168)
(99,60)
(100,150)
(101,25)
(102,36)
(103,104)
(104,42)
(105,40)
(106,54)
(107,36)
(108,36)
(109,54)
(110,30)
(111,76)
(112,24)
(113,38)
(114,36)
(115,120)
(116,21)
(117,84)
(118,87)
(119,72)
(120,60)
(121,55)
(122,30)
(123,20)
(124,15)
(125,250)
(126,24)
(127,128)
(128,96)
(129,44)
(130,210)
(131,65)
(132,60)
(133,72)
(134,204)
(135,180)
(136,18)
(137,138)
(138,24)
(139,23)
(140,120)
(141,16)
(142,105)
(143,70)
(144,12)
(145,70)
(146,222)
(147,56)
(148,114)
(149,74)
(150,300)
(151,25)
(152,18)
(153,36)
(154,120)
(155,30)
(156,84)
(157,158)
(158,39)
(159,108)
(160,120)
(161,24)
(162,108)
(163,164)
(164,60)
(165,20)
(166,84)
(167,168)
(168,24)
(169,182)
(170,90)
(171,36)
(172,132)
(173,174)
(174,84)
(175,200)
(176,60)
(177,116)
(178,66)
(179,89)
(180,60)
(181,45)
(182,168)
(183,60)
(184,24)
(185,190)
(186,60)
(187,90)
(188,48)
(189,72)
(190,90)
(191,95)
(192,48)
(193,194)
(194,294)
(195,140)
(196,168)
(197,198)
(198,60)
(199,11)
(200,150)
(201,68)
(202,75)
(203,56)
(204,36)
(205,20)
(206,312)
(207,24)
(208,84)
(209,45)
(210,120)
(211,21)
(212,54)
(213,140)
(214,36)
(215,220)
(216,36)
(217,120)
(218,54)
(219,148)
(220,30)
(221,126)
(222,228)
(223,224)
(224,24)
(225,300)
(226,114)
(227,228)
(228,36)
(229,57)
(230,120)
(231,40)
(232,42)
(233,26)
(234,84)
(235,80)
(236,87)
(237,156)
(238,72)
(239,119)
(240,60)
(241,120)
(242,165)
(243,324)
(244,30)
(245,280)
(246,60)
(247,126)
(248,30)
(249,84)
(250,750)
(251,125)
(252,24)
(253,120)
(254,384)
(255,180)
(256,192)
(257,258)
(258,132)
(259,152)
(260,210)
(261,84)
(262,195)
(263,88)
(264,60)
(265,270)
(266,72)
(267,44)
(268,204)
(269,134)
(270,180)
(271,135)
(272,36)
(273,56)
(274,138)
(275,50)
(276,24)
(277,278)
(278,69)
(279,60)
(280,120)
(281,28)
(282,48)
(283,284)
(284,105)
(285,180)
(286,210)
(287,40)
(288,24)
(289,306)
(290,210)
(291,196)
(292,222)
(293,294)
(294,168)
(295,290)
(296,114)
(297,180)
(298,222)
(299,168)
(300,300)
(301,88)
(302,75)
(303,100)
(304,36)
(305,30)
(306,36)
(307,44)
(308,120)
(309,104)
(310,30)
(311,155)
(312,84)
(313,314)
(314,474)
(315,120)
(316,39)
(317,318)
(318,108)
(319,35)
(320,240)
(321,36)
(322,24)
(323,18)
(324,108)
(325,350)
(326,492)
(327,108)
(328,60)
(329,16)
(330,60)
(331,55)
(332,84)
(333,228)
(334,168)
(335,340)
(336,24)
(337,338)
(338,546)
(339,76)
(340,90)
(341,15)
(342,36)
(343,392)
(344,132)
(345,120)
(346,174)
(347,116)
(348,84)
(349,87)
(350,600)
(351,252)
(352,120)
(353,118)
(354,348)
(355,70)
(356,66)
(357,72)
(358,267)
(359,179)
(360,60)
(361,171)
(362,45)
(363,220)
(364,168)
(365,370)
(366,60)
(367,368)
(368,24)
(369,60)
(370,570)
(371,216)
(372,60)
(373,374)
(374,90)
(375,500)
(376,48)
(377,14)
(378,72)
(379,189)
(380,90)
(381,128)
(382,285)
(383,384)
(384,96)
(385,40)
(386,582)
(387,132)
(388,294)
(389,194)
(390,420)
(391,72)
(392,168)
(393,260)
(394,198)
(395,390)
(396,60)
(397,398)
(398,33)
(399,72)
(400,300)
(401,100)
(402,204)
(403,210)
(404,75)
(405,540)
(406,168)
(407,190)
(408,36)
(409,204)
(410,60)
(411,276)
(412,312)
(413,232)
(414,24)
(415,420)
(416,168)
(417,92)
(418,45)
(419,209)
(420,120)
(421,42)
(422,21)
(423,48)
(424,54)
(425,450)
(426,420)
(427,120)
(428,36)
(429,140)
(430,660)
(431,215)
(432,36)
(433,434)
(434,120)
(435,140)
(436,54)
(437,72)
(438,444)
(439,219)
(440,30)
(441,168)
(442,126)
(443,444)
(444,228)
(445,110)
(446,672)
(447,148)
(448,48)
(449,224)
(450,300)
(451,20)
(452,114)
(453,100)
(454,228)
(455,280)
(456,36)
(457,458)
(458,57)
(459,36)
(460,120)
(461,23)
(462,120)
(463,464)
(464,84)
(465,60)
(466,78)
(467,468)
(468,84)
(469,136)
(470,240)
(471,316)
(472,174)
(473,220)
(474,156)
(475,450)
(476,72)
(477,108)
(478,357)
(479,239)
(480,120)
(481,266)
(482,120)
(483,24)
(484,165)
(485,490)
(486,324)
(487,488)
(488,30)
(489,164)
(490,840)
(491,245)
(492,60)
(493,126)
(494,126)
(495,60)
(496,60)
(497,280)
(498,84)
(499,249)
(500,750)
(501,168)
(502,375)
(503,504)
(504,24)
(505,50)
(506,120)
(507,364)
(508,384)
(509,127)
(510,180)
(511,296)
(512,384)
(513,36)
(514,258)
(515,520)
(516,132)
(517,80)
(518,456)
(519,348)
(520,210)
(521,13)
(522,84)
(523,524)
(524,195)
(525,200)
(526,264)
(527,90)
(528,60)
(529,552)
(530,270)
(531,348)
(532,72)
(533,140)
(534,132)
(535,180)
(536,204)
(537,356)
(538,402)
(539,280)
(540,180)
(541,45)
(542,135)
(543,180)
(544,72)
(545,270)
(546,168)
(547,548)
(548,138)
(549,60)
(550,150)
(551,63)
(552,24)
(553,312)
(554,834)
(555,380)
(556,69)
(557,62)
(558,60)
(559,308)
(560,120)
(561,180)
(562,84)
(563,188)
(564,48)
(565,190)
(566,852)
(567,216)
(568,210)
(569,284)
(570,180)
(571,285)
(572,210)
(573,380)
(574,120)
(575,600)
(576,48)
(577,578)
(578,306)
(579,388)
(580,210)
(581,168)
(582,588)
(583,270)
(584,222)
(585,420)
(586,294)
(587,588)
(588,168)
(589,45)
(590,870)
(591,396)
(592,228)
(593,594)
(594,180)
(595,360)
(596,222)
(597,44)
(598,168)
(599,299)
(600,300)
(601,300)
(602,264)
(603,204)
(604,75)
(605,110)
(606,300)
(607,608)
(608,72)
(609,56)
(610,30)
(611,112)
(612,36)
(613,614)
(614,132)
(615,20)
(616,120)
(617,618)
(618,312)
(619,103)
(620,30)
(621,72)
(622,465)
(623,88)
(624,84)
(625,1250)
(626,942)
(627,180)
(628,474)
(629,342)
(630,120)
(631,315)
(632,78)
(633,84)
(634,318)
(635,640)
(636,108)
(637,56)
(638,105)
(639,420)
(640,480)
(641,320)
(642,36)
(643,644)
(644,24)
(645,220)
(646,18)
(647,648)
(648,108)
(649,145)
(650,1050)
(651,120)
(652,492)
(653,654)
(654,108)
(655,130)
(656,60)
(657,444)
(658,48)
(659,329)
(660,60)
(661,110)
(662,165)
(663,252)
(664,84)
(665,360)
(666,228)
(667,168)
(668,168)
(669,224)
(670,1020)
(671,30)
(672,24)
(673,674)
(674,1014)
(675,900)
(676,546)
(677,226)
(678,228)
(679,392)
(680,90)
(681,228)
(682,15)
(683,684)
(684,36)
(685,690)
(686,1176)
(687,228)
(688,132)
(689,378)
(690,120)
(691,69)
(692,174)
(693,120)
(694,348)
(695,230)
(696,84)
(697,180)
(698,87)
(699,52)
(700,600)
(701,350)
(702,252)
(703,342)
(704,240)
(705,80)
(706,354)
(707,200)
(708,348)
(709,59)
(710,210)
(711,156)
(712,66)
(713,120)
(714,72)
(715,70)
(716,267)
(717,476)
(718,537)
(719,359)
(720,60)
(721,104)
(722,171)
(723,120)
(724,45)
(725,350)
(726,660)
(727,728)
(728,168)
(729,972)
(730,1110)
(731,396)
(732,60)
(733,734)
(734,1104)
(735,280)
(736,24)
(737,340)
(738,60)
(739,369)
(740,570)
(741,252)
(742,216)
(743,248)
(744,60)
(745,370)
(746,1122)
(747,84)
(748,90)
(749,72)
(750,1500)
(751,375)
(752,48)
(753,500)
(754,42)
(755,50)
(756,72)
(757,758)
(758,189)
(759,120)
(760,90)
(761,190)
(762,384)
(763,216)
(764,285)
(765,180)
(766,384)
(767,406)
(768,192)
(769,96)
(770,120)
(771,516)
(772,582)
(773,774)
(774,132)
(775,150)
(776,294)
(777,152)
(778,582)
(779,180)
(780,420)
(781,35)
(782,72)
(783,252)
(784,168)
(785,790)
(786,780)
(787,788)
(788,198)
(789,88)
(790,390)
(791,152)
(792,60)
(793,210)
(794,1194)
(795,540)
(796,33)
(797,114)
(798,72)
(799,144)
(800,600)
(801,132)
(802,300)
(803,370)
(804,204)
(805,120)
(806,210)
(807,268)
(808,150)
(809,101)
(810,540)
(811,135)
(812,168)
(813,540)
(814,570)
(815,820)
(816,36)
(817,396)
(818,204)
(819,168)
(820,60)
(821,410)
(822,276)
(823,824)
(824,312)
(825,100)
(826,696)
(827,828)
(828,24)
(829,138)
(830,420)
(831,556)
(832,336)
(833,504)
(834,276)
(835,840)
(836,45)
(837,180)
(838,627)
(839,419)
(840,120)
(841,203)
(842,42)
(843,28)
(844,21)
(845,910)
(846,48)
(847,440)
(848,108)
(849,284)
(850,450)
(851,456)
(852,420)
(853,854)
(854,120)
(855,180)
(856,36)
(857,858)
(858,420)
(859,39)
(860,660)
(861,40)
(862,645)
(863,864)
(864,72)
(865,870)
(866,1302)
(867,612)
(868,120)
(869,195)
(870,420)
(871,476)
(872,54)
(873,588)
(874,72)
(875,1000)
(876,444)
(877,878)
(878,219)
(879,588)
(880,60)
(881,88)
(882,168)
(883,884)
(884,126)
(885,580)
(886,444)
(887,888)
(888,228)
(889,128)
(890,330)
(891,540)
(892,672)
(893,144)
(894,444)
(895,890)
(896,96)
(897,168)
(898,672)
(899,105)
(900,300)
(901,54)
(902,60)
(903,88)
(904,114)
(905,90)
(906,300)
(907,908)
(908,228)
(909,300)
(910,840)
(911,35)
(912,36)
(913,420)
(914,1374)
(915,60)
(916,57)
(917,520)
(918,36)
(919,51)
(920,120)
(921,44)
(922,69)
(923,70)
(924,120)
(925,950)
(926,1392)
(927,312)
(928,168)
(929,464)
(930,60)
(931,504)
(932,78)
(933,620)
(934,468)
(935,90)
(936,84)
(937,938)
(938,408)
(939,628)
(940,240)
(941,235)
(942,948)
(943,120)
(944,348)
(945,360)
(946,660)
(947,948)
(948,156)
(949,518)
(950,450)
(951,636)
(952,72)
(953,106)
(954,108)
(955,190)
(956,357)
(957,140)
(958,717)
(959,552)
(960,240)
(961,465)
(962,798)
(963,36)
(964,120)
(965,970)
(966,24)
(967,88)
(968,330)
(969,36)
(970,1470)
(971,485)
(972,324)
(973,184)
(974,1464)
(975,700)
(976,60)
(977,326)
(978,492)
(979,110)
(980,840)
(981,108)
(982,735)
(983,984)
(984,60)
(985,990)
(986,126)
(987,16)
(988,126)
(989,264)
(990,60)
(991,99)
(992,120)
(993,220)
(994,840)
(995,110)
(997,998)
(998,249)
(999,684)
(1000,750)
