Professor Ming-Chia Li

Contact

• Email: mcli@math.nctu.edu.tw
• Tel: +886-3-571-2121 ext. 56463
• Fax: +886-3-572-4679
• Address: Department of Applied Mathematics, National Yang Ming Chiao Tung University,1001 Ta Hsueh Road, Hsinchu, Taiwan 30050, ROC

Teaching

• Fall Semester, 2024：
  • Differential Equations
  • An Introduction to Dynamical System
  • Introduction to Analysis (I)
• Spring Semester, 2024：
  • Introduction to Analysis (II)

Vitae

• Education
  • Ph. D. in Mathematics, Northwestern Univ. (1997)
• Research Areas
  • Dynamical System
  • Differential Equations
• Positions, Honors and Awards
  • Assistant Professor, Department of Mathematics National Changhua University of Education ( 08/1997 - 07/2000 )
  • Associate Professor, Department of Mathematics National Changhua University of Education ( 08/2000 - 07/2004 )
  • Professor, Department of Mathematics National Changhua University of Education ( 08/2004 - 07/2005 )
  • Professor, Department of Applied Mathematics National Chiao Tung University ( 08/2005 - )
• Recent Research Projects
  • Chaotic embedding and global implicit function theorem II (NSC 102-2115-M-009 -008 -MY2) 
  • Chaotic embedding and global implicit function theorem (NSC 101-2115-M-009-005-)
  • Chaotic dynamics of high-dimensional systems perturbed from low-dimensional ones (NSC 99-2115-M-009-004-MY2)
  • Chaotic dynamics of perturbed singular difference equations (2/2) (NSC 95-2115-M-018-004)
  • Chaotic dynamics of perturbed singular difference equations (1/2) (NSC 94-2115-M-018-006)
  • The nonwandering set of dynamical systems on noncompact space (2/2) (NSC 93-2115-M-018-001)
  • The nonwandering set of dynamical systems on noncompact space (1/2) (NSC 92-2115-M-018-002)
  • Chaos in low dimensional dynamical systems (2/2) (NSC 91-2115-M-018-002)

Selected Publications

(A)   Refereed Papers：

1. M.-C. Li, 1997, Structural stability of Morse-Smale gradient-like flows under discretizations, SIAM J. Mathematical Analysis, 28, pp. 381-388.
2. M.-C. Li, 1997, Structural stability of flows under numerics, J. Differential Equations, 141, pp. 1-12.
3. M.-C. Li, 1999, Structural stability on basins for numerical methods, Proc. Amer. Math. Soc., 127, pp. 289-295.
4. M.-C. Li, 1999, Structural stability for the Euler method, SIAM J. Mathematical Analysis, 30, pp. 747-755.
5. M.-C. Li, 1999, Global stability of numerical ordinary differential equations, in Dynamical Systems (edited by Y, Jiang and L. Wen), World Scientific, London, pp. 160-164.
6. M.-C. Li, 2000, Stability of diffeomorphisms along one parameter, Rocky Mount. J. Math., 30, pp. 641-649.
7. M.-C. Li, 2000, Period three orbits for the quadratic family, Far East J. Dynamical Systems, 2, pp. 99-105.
8. M.-C. Li, 2001, Conjugacy or semi-conjugacy between logistic and tent maps, Far East J. Dynamical Systems, 3 (1), pp. 1-8.
9. C.-H. Hsu and M.-C. Li, 2002, Transitivity implies period six: a simple proof, American Mathematical Monthly, 109, pp. 840-843.
10. M.-C. Li, 2001, Transitivity and a periodic point do not imply sensitivity, Far East J. Dynamical Systems, 3 (2), pp. 169-174.
11. M.-C. Li, 2002, Normal hyperbolicity for flows and numerical methods, Rocky Mount. J. Math., 32, pp. 349-356.
12. M.-C. Li, 2002, A simple proof that homoclinicity implies horseshoe for continuous interval maps, International J. Pure and Applied Math., 1, pp. 373-377.
13. M.-C. Li and M. Malkin, 2002, Smooth symmetric models for unimodal maps, in Progress in Nonlinear Science, Volume I: Mathematical Problems in Nonlinear Dynamics, Proceedings of the International Conference dedicated to the 100th Anniversary of A. A. Andronov, Nizhny Novgorod, July 2-6, 2001", pp. 296-307.
14. M.-C. Li, 2003, Nondegenerate homoclinic tangency and hyperbolic sets, Nonlinear Analysis, 52, pp. 1521-1533.
15. M.-C. Li and M. Malkin, 2004, Lorenz models for symmetric unimodal maps, Second International Congress of Chinese Mathematicians, Proceedings of ICCM 2001, December 17-22, 2001, The Grand Hotel, Taipei, Taiwan (C.S. Lin, L. Yang and S.T. Yau, eds.), International Press, pp.651-657.
16. M.-C. Li, 2003, Point bifurcations and bubbles for a cubic family , J. Difference Equations and Applications, 9, pp. 553-558.
17. B.-S. Du, S.-S. Huang and M.-C. Li, 2003, Generalized Fermat, double Fermat and Newton sequences, J. Number Theory , 98, pp. 172-183.
18. M.-R. Chen and M.-C. Li, 2002, The limits sets of the Euler method with variable stepsizes, Far East J. Dynamical systems, 4, pp. 17-25.
19. M.-C. Li and M. Malkin, 2003, Smooth symmetric and Lorenz models for unimodal maps, Intern. J. Bifurcation and Chaos, 13, pp.3353-3371.
20. B.-S. Du and M.-C. Li, 2003, A refinement of Sharkovskii's theorem on orbit types characterized by two parameters, J. Math. Anal. Appl., 278, pp. 77-82.
21. M.-C. Li, 2003, Stability of parameterized Morse-Smale gradient-like flows, Discrete and Continuous Dynamical Systems, 9, pp. 1073-1077.
22. M.-C. Li, 2003, Persistence of normal hyperbolicity for partial differential equations under discretizations, Z. Angew. Math. Mech., 83, pp. 564-566.
23. S.-B. Hsu, M.-C. Li, W. Liu and M. Malkin, 2003, Heteroclinic foliation, global oscillations for the Nicholson-Bailey model and delay of stability loss, Discrete and Continuous Dynamical Systems, 9, pp.1465-1492.
24. M.-C. Li and C.-W. Yu, 2003, Chaotic dynamics of a generalized cobweb model, WSEAS Transactions on Mathematics, 2, pp.188-193.
25. M.-C. Li and M. Malkin, 2004, Bounded nonwandering sets for polynomial maps, Journal of Dynamical and Control Systems, 10, pp.377-389.
26. M. Chen and M.-C. Li, 2004, Stability of uniformly Morse-Smale gradient-like numerical methods for flows, IMA J. Numerical Analysis, 24, pp.577-585.
27. M.-C. Li, 2004, Qualitative property between flows and numerical methods, Nonlinear Analysis, 59, 771-787.
28. M.-C. Li, 2005, Stability of a saddle node bifurcation under numerical approximations, Computers and Mathematics with Applications, , 49, 1849-1852.
29. B.-S. Du, S.-S. Huang, and M.-C. Li, 2005, Newton, Fermat, and exactly realizable sequences, Journal of Integer Sequences, 8, Article 05.1.2
30. H.-J. Chen and M.-C. Li, 2006, Imperfect capital mobility and chaotic dynamics of the real exchange rate, Taiwan Economic Review, 34, 373-391.
31. B.-S. Du, M.-C. Li and M. Malkin, 2006, Topological horseshoes for Arneodo-Coullet-Tresser maps, Regular and Chaotic Dynamics, 11, 181-190.
32. M.-C. Li and M. Malkin, 2006, Topological horseshoes for perturbations of singular difference equations, Nonlinearity, 19, 795-811.
33. B.-S. Du, S.-R. Hsiau, M.-C. Li, and M. Malkin, 2007, An improved stability criterion with application to the Arneodo-Coullet-Tresser map, Taiwanese J. Math., 11, 1369-1382.
34. H.-J. Chen and M.-C. Li, 2008, Chaotic dynamics in a monetary economy with habit persistence, Journal of Economic Behavior and Organization, 65, 245-260.
35. H.-J. Chen, M.-C. Li and Y.-J. Lin, 2008, Chaotic dynamics in an overlapping generations model with myopic and adaptive expectations, Journal of Economic Behavior and Organization, 67, 48-56.
36. H.-J. Chen and M.-C. Li, 2008, Productive public expenditures, expectation formations and nonlinear dynamics, Mathematical Social Sciences, 56, 109-126 .
37. J. Juang, M.-C. Li, and M. Malkin, 2008, Chaotic difference equations in two variables and their multidimensional perturbations, Nonlinearity, 21, 1019-1040.
38. S. Gonchenko, M.-C. Li and M. Malkin, 2008, Generalized Henon maps and Smale horseshoes of new types, Intern. J. Bifurcation and Chaos, 18, 3029-3052.
39. H.-J. Chen and M.-C. Li, 2008, Human capital externality and chaotic equilibrium dynamics, Mathematical and Computer Modelling of Dynamical Systems, 14, 571-586.
40. M.-C. Li, M.-J. Lyu  and P. Zgliczynski, 2008, Topological entropy for multidimensional perturbations of snap-back repellers and one-dimensional maps, Nonlinearity, 2555-2567. 
41. S.-M. Chang, M.-C. Li and W.-W. Lin, 2009, Asymptotic synchronization of modified logistic hyper-chaotic systems and its applications, Nonlinear Analysis-Real World Applicaions, 10, 869-880.
42. M.-C. Li and M.-J. Lyu, 2009, A simple proof for persistence of snap-back repellers, Journal of Mathematical Analysis and Applications, 352, 669-671.
43. H.-J. Chen and M.-C. Li, 2009, Habit formation and chaotic dynamics in an n-dimensional cash-in-advance economy, Nonlinear Dynamics, 58, 49-62.
44. M.-C. Li and P. Zgliczynski, 2009, On stability of forcing relations for multidimensional perturbations of interval maps, Fundamenta Mathematicae, 206, 241-251.
45. S. Gonchenko, M.-C. Li, 2010, Shilnikov's cross-map method and hyperbolic dynamics of three-dimensional Henon-like maps, Regular and Chaotic Dynamics, 15, 165-184.
46. M.-C. Li and M. Malkin, 2010, Approximation of entropy on hyperbolic sets for one-dimensional maps and their multidimensional perturbations, Regular and Chaotic Dynamics, 15, 210-221.
47. S. Kiriki, M.-C. Li and T. Soma, 2010, Coexistence of invariant sets with and without SRB measures in Henon family, Nonlinearity, 23, 2253-2269
48. H.-J. Chen and M.-C. Li, 2011, Environmental tax policy, habit formation and nonlinear dynamics, Nonlinear Analysis-Real World Applications, 12, 246-253.
49. M.-C. Li and M.-J. Lyu, 2011, Topological dynamics for multidimensional perturbations of maps with covering relations and Liapunov condition, Journal of Differential Equations, 250, 799-812.
50. M.-C. Li and M.-J. Lyu, 2011, Positive topological entropy for multidimensional perturbations of topologically crossing homoclinicity, Discrete and Continuous Dynamical Systems, ser. A, 20, 243-252.
51. L. Bunimovich, M.-C. Li and M.-J. Lyu, 2012, Covering relations for coupled map networks, Journal of Mathematical Analysis and Applications, 396, 189-198.
52. H.-J. Chen and M.-C. Li, 2013, Child allowances, fertility and chaotic dynamics, Chaos, 23, 023106-023106-9.
53. M.-C. Li, 2014, An elementary proof of a generalization of Banach's mapping theorem, American Mathematical Monthly, 121, 445-446.
54. H.-J. Chen and M.-C. Li, 2015, Stability of symbolic embeddings for difference equations and their multidimensional perturbations,Journal of Differential Equations, 258, 906-918.
55. M.-C. Li and M.-J. Lyu, 2016, Covering relations and Lyapunov condition for topological conjugacy, Dynamical Systems, 31, 60-78.
56. M.-C. Li and M.-J. Lyu, 2016, Topological conjugacy for Lipschitz perturbations of non-autonomous systems, Discrete and Continuous Dynamical System - A, 36(9), 5011-5024.
57. S. Kiriki, M.-C. Li, and T. Soma, 2016, Geometric Lorenz flows with historic behavior, Discrete and Continuous Dynamical System - A, 36(12), 7021-7028.
58. H.-J. Chen, M.-C. Li and S.-X. Lin, Chaos for implicit difference equations with snap-back repellers, Journal of Difference Equations and Applications, accepted.
59. S. Gonchenko, M.-C. Li, and M. Malikin, Criteria on existence of horseshoes near homoclinic tangencies of arbitrary orders, Dynamical Systems, accepted.
60. Chen, H.-J., Li, M.-C., Lin, S.-X. Chaos for implicit difference equations with snap-back repellers. J. Difference Equ. Appl., 24 (2018), 180-191
61. Sergey Gonchenko, Ming-Chia Li & Mikhail Malkin, Criteria on existence of horseshoes near homoclinic tangencies of arbitrary orders. Dynamical Systems, Dyn. Syst. 33 (2018), 441–463.
62. Li, Ming-Chia, Stretches across for chaos. Chaos 29 (2019), 053127
63. Li, Ming-Chia, On the Banach mapping theorem and a related conjecture, Rocky Mountain J. Mathematics 52 (2022), 183-187.
64. F. Cavalli, H.-J. Chen, M.-C. Li, A. Naimzada, N. Pecora, Heterogeneous expectations and equilibria selection in an evolutionary overlapping generations model, Journal of Mathematical Economics, 104 (2023), article 102806.

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