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研究生:藍智偉
研究生(外文):Chih-Wei Lan
論文名稱:數值研究Mira Map 驟回排斥子存在性
論文名稱(外文):Numerical study Existence of Snapback Repellers for Mira Map
指導教授:彭振昌
指導教授(外文):Chen-Chang Peng
學位類別:碩士
校院名稱:國立嘉義大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
畢業學年度:104
語文別:中文
中文關鍵詞:驟回排斥子混沌Mira map映射電腦輔助證明虛擬弧長延拓法
外文關鍵詞:Snapback RepellersChaosMira mapComputer-assisted proofPseudo Arc-length Continuation method
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本論文主要探討二維單參數不可逆動態系統米拉映射驟回排斥子的存在性。我們不難看出米拉映射反可積分極限參數的存在性。根據陳-林-彭結果,可知在反可積分極限附近存在驟回排斥子。本論文以反可積分極限附近為出發點,利用虛擬孤長延拓法與電腦輔助證明,我們可以證明米拉映射在遠離反可積分極限仍存在驟回排斥子。進一步我們由數值結果呈現臨界驟回排斥子的存在性與分歧現象。
In this paper we study the existence of snapback repellers for a 2-dimensional one-parameter noninvertible dynamical system-Mira map. It is not difficult to see the existence of anti-integrable limits. According to the results of Chen-Lin-Peng, they proved the existence of snapback repellers near anti-integrable limits. Employing the pseudo-arclength continuation method and computer-assisted proofs, we prove the existence of snapback repellers on some intervals away from anti-integrable limits. Furthermore, we also show the existence of critical snapback repellers and bifurcation phenomena from our numerical results.
Contents
Abstract(Chinese)i

Abstract(English) ii
Acknowledgements iii

Contents iv

1. Introduction 1

2. Preliminaries 6

2.1 Existence of snapback repellers when parameter values are fixed. ... 9

2.2 Continuation methods and existence of snapback repellers when parameter values are varied. ... 10

3. Study the Existence of Snapback Repellers for Mira map 13

Reference 23
[1] S. Aubry. and G. Abramovici. Chaotic trajectories in the standard map. The concept of anti-integrability, Phys. D, 43 (1990), 199-210.

[2] S. J. Aubry. Anti-integrability in dynamical and variational problems. Phys. D, 86 (1995), 284-296.

[3] J. Banks, J. Brooks, G. Cairns, G. Davis, P. Stacey. On Devaney's denition of chaos. The American Mathematical Monthly, 99 (1992), 332-334.

[4] T. H. Chen, W. W. Lin and C. C. Peng. Chaotic orbits for dierentiable maps near anti-integrable limits. Journal of Mathematical Analysis and Applications,
435 (2016), 889-916.

[5] G. Chen, S. B. Hsu, and J. Zhou. Snapback repellers as a cause of chaotic vibration of the wave equation with a van der pol boundary condition and energy
injection at the middle of the span. Journal of Mathematical Physics, 39 (1998),
6459-6489.

[6] R. L. Devaney. An Introduction to Chaotic Dynamical Systems. Second Edition.
Addison-Wesley, Redwood City, Canada, 1989.

[7] Jerrold E. Marsden Michael J. Homan. Elementary Classical Analysis. Second
Edition. W. H. Freeman and Company, New York, 1993.

[8] Ott, Edward. Chaos in Dynamical Systems. Cambridge University Press, (1994).

[9] L. Gardinia, I. Sushkob, V. Avrutinc and M. Schanzc. Critical homoclinic orbits lead to snap-back repellers. Chaos, Solitons and Fractals, 44 (2011), 433-449.

[10] R. Krawczyk. Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehler-schranken. Computing, 4 (1969), 187-201.

[11] U. Kirchgraber and D. Stoer. Transversal homoclinic points of the H^enon
map. Annali di Matematica, 185 (2006), 187-204.

[12] Bernd Krauskopf, Hinke M. Osinga, Jorge Galan-Vioque (Eds.). Numerical Continuation Methods for Dynamical Systems. Published by Springer.

[13] Tien-Yien Li and James A. Yorke. Period three implies chaos. The American Mathematical Monthly, 82 (1975), 985-992.

[14] R. E. Moore. A test for existence of solutions for nonlinear systems. SIAM J.
Numer. Anal., 4 (1977), 611-615.

[15] R. E. Moore. Interval Analysis. Prentice-Hall, Englewood Clis, NJ, 1966.

[16] F. R. Marotto. Snap-back repellers imply chaos in Rn. J. Math. Anal. Appl., 63 (1978), 199 - 223.

[17] F. R. Marotto. On redening a snap-back repeller. Chaos, Solitons and Fractals, 25 (2005), 25-28.

[18] C. Mira, L. Gardini, A. Barugolo and J. C. Cathala. Chaotic Dynamics in Two-Dimensional Noninvertible Map. New Jersey : World Scientic, 1996.

[19] C. Ryan Gwaltney, Youdong Lin, Luke D. Simoni and Mark A. Stadtherr. Interval Methods for Nonlinear Equation Solving Applications. Department of Chemical and Biomolecular Engineering, University of Notre Dame Notre Dame, IN 46556, USA.

[20] D. Sterling and J. D. Meiss. Computing periodic orbits using the anti-integrable limit. Physics Letters A, 241 (1998), 46-52.

[21] S. M. Rump. INTLAB|INTerval LABoratory. In Tibor Csendes, Editor' Developments in Reliable Computing. Kluwer, Dordrecht (1999), 77-104.

[22] Smale, Stephen. Dierentiable dynamical systems. Bull. Amer. Math. Soc., 73 (1967), 747-817.

[23] Endre Suli and David Mayers. An Introduction to Numerical Analysis. Cambridge
University Press, 2003.
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