Acta mathematica scientia,Series A ›› 1999, Vol. 19 ›› Issue (2): 233-240.
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Abstract:
Appling the KAM theorem of reversible map in [1],we prove that in certain conditions,for reversible map on R3, there exists invariant conic surface near fixed point. We prove there exists this kind of invariant conic surface for Fibonacci map.
Key words: Ｒｅｖｅｒｓｉｂｌｅ, ＫＡＭｔｈｅｏｒｅｍ, Ｉｎｖａｒｉａｎｔｃｏｎｉｃｓｕｒｆａｃｅ, Ｄｉｏｐｈａｎｔｉｎｅｃｏｎｄｉｔｉｏｎ
CLC Number:
Liu Qinghui. Invariant conic surface of fibonacci trace map[J].Acta mathematica scientia,Series A, 1999, 19(2): 233-240.
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URL: http://actams.apm.ac.cn/sxwlxbA/EN/
http://actams.apm.ac.cn/sxwlxbA/EN/Y1999/V19/I2/233
１ Ｓｅｖｒｙｕｋ Ｍ．ＲｅｖｅｒｓｉｂｌｅＳｙｓｔｅｍ，ＬｅｃｔＮｏｔｅＭａｔｈ，１９８６，１２１１ ２ ＰｅｙｒｉéｒｅＪ，ＷｅｎＺＸ，ＷｅｎＺＹ．Ｏｎｔｈｅｄｙｎａｍｉｃｂｅｈａｖｉｏｕｒｓｏｆｔｈｅｉｔｅｒａｔｉｏｎｓｏｆｔｈｅｔｒａｃｅｍａｐａｓｓｏｃｉａｔｅｄｗｉｔｈｓｕｂｓｔｉｔｕｔｉｖｅｓｅｑｕｅｎｃｅｓ．Ｉｎ：ｅｄ．Ｓ．Ｘｉａｏ，Ｘ Ｈｕ．Ｎｏｎｌｉｎｅａｒｐｒｏｂｌｅｍｓｉｎｅｎｇｉｎｅｅｒｉｎｇａｎｄｓｃｉｅｎｃｅ．Ｂｅｉｊｉｎｇ：ＳｃｉｅｎｃｅＰｒｅｓｓ１９９２，２５９－２６６ ３ ＰｅｙｒｉéｒｅＪ，ＷｅｎＺＸ，ＷｅｎＺＹ．Ｐｏｌｙｎｏｍéｓａｓｓｏｃｉéｅｓａｕｘｅｎｄｏｍｏｒｐｈｉｓｍｅｓｄｅｇｒｏｕｐｅｓｌｉｂｒｅｓ．Ｌ＇Ｅｎｓｅｉｇ Ｍａｔｈ，１９９３：３９：１５３－１７５ ４ ＲｏｂｅｒｔＪ，ＢａａｋｅＭ．Ｔｒａｃｅｍａｐｓａｓ３Ｄｒｅｖｅｒｓｉｂｌｅｄｙｎａｍｉｃａｌｓｙｓｔｅｍｓｗｉｔｈａｎｉｎｖａｒｉａｎｔ．ＪＳｔａｔＰｈｙｓ，１９９４，７４（３） ５ ＷａｎＹ Ｈ．ＣｏｍｐｕｔａｔｉｏｎｓｏｆｔｈｅｓｔａｂｉｌｉｔｙｃｏｎｄｉｔｉｏｎｆｏｒｔｈｅＨｏｐｆｂｉｆｕｒｃａｔｉｏｎｏｆｄｉｆｆｅｏｍｏｒｐｈｉｓｍｓｏｎR2．ＳＩＡＭ ＪＡｐｐｌＭａｔｈ，１９７８，３４：１６７－１７５ ６ ＧｕｃｋｅｎｈｅｉｍｅｒＪ，ＨｏｌｍｅｓＰ．ＮｏｎｌｉｎｅａｒＯｓｃｉｌｌａｔｉｏｎｓ，ＤｙｎａｍｉｃａｌＳｙｓｔｅｍｓ，ａｎｄＢｉｆｕｒｃａｔｉｏｎｏｆＶｅｃｔｏｒＦｉｅｌｄｓ．Ｎｅｗ ＹｏｒｋＨｅｉｄｅｌｂｅｒｇ，Ｂｅｒｌｉｎ：ＳｐｒｉｎｇｅｒＶｅｒｌａｇ：１９８３ ７ 朱德明，韩茂安．光滑动力系统．华东师范大学出版社，１９９３
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