• ycchen$\color{red}{@}$math.sinica.edu.tw
• +886 2 2368-5999 ext. 630
• +886 2 2368-9771

• 混沌動力系統

• PhD in Applied Mathematics and Theoretical Physics 英國劍橋大學 (2002)
• Certificate of Advanced Study in Mathematics (Part III) DAMTP, 英國劍橋大學 (1997)
• MSc in Physics 台灣大學 (1993)
• BSc in Physics 中央大學 (1991)

• Associate Research Fellow Institute of Mathematics, Academia Sinica 2013 - Present
• Associate Editor International Journal of Bifurcation and Chaos 2012 - Present
• Adjunct Assistant Professor Department of Applied Mathematics, National Chiao Tung Univ, Taiwan 2010/8 - 2011/7
• Curator Scholarpedia-the free peer reviewed encyclopedia 2007/8 - Present
• Assistant Research Fellow Institute of Mathematics, Academia Sinica 2006 - 2013
• Adjunct Lecturer Department of Mathematics, National Taiwan Univ 2005/8 - 2006/7
• Regular Postdoctoral Fellow Institute of Mathematics (Postdoctoral Fellows Program at Academia Sinica) 2004 - 2006
• Postdoctoral Fellow Institute of Mathematics, Academia Sinica 2002 - 2004

Research interests: Dynamical Systems, in  particular,  anti-integrable limits, arithmetic dynamics, billiard systems, chaos, Hamiltonian dynamics, Hénon maps, slow-fast systems, quadratic maps.

1. "Holomorphic shadowing for Henon maps revisited: an implicit function theorem perspective" , Preprint , 2022. (24 pages)
2. (with T Kawahira) "From hyperbolic to parabolic parameters along internal rays" , Preprint , 2022. (40 pages)
3. "Persistence of hyperbolic invariant sets for shift-like diffeomorphisms" , Preprint , 2021. (42 pages)
4. (with T Kawahira) "From Cantor to semi-hyperbolic parameters along external rays" , Transactions of the American Mathematical Society , 372, 7959-7992, 2019.
5. "Transitions and anti-integrable limits for multi-hole Sturmian systems and Denjoy counterexamples" , Transactions of Mathematics and Its Applications , 3, tnz002-, 2019.
6. (with T Kawahira) "Simple proofs for the derivative estimates of the holomorphic motion near two boundary points of the Mandelbrot set" , Journal of Mathematical Analysis and Applications , 473, 345-356, 2019.
7. "A proof of Devaney-Nitecki region for the Henon mapping using the anti-integrable limit" , Advances in Dynamical Systems and Applications , 13, 33-43, 2018.
8. (with Q Yang, B Ling, W Liu) "On the distal and asymptotic sets for β-transformations" , Journal of Mathematical Analysis and Applications , 464, 188-200, 2018.
9. (with W-T Lin) "Family of Smale-Williams solenoid attractors as solutions of differential equations: exact formula and conjugacy" , International Journal of Bifurcation and Chaos , 25, 1550137001-1550137009, 2015.
10. "Abrupt bifurcation, chaotic scattering, and anti-integrable limit" , RIMS Kokyuroku , 1901, 47-54, 2014.
11. (with S-S Chen, J-M Yuan) "Topological horseshoes in travelling waves of discretized nonlinear wave equations" , Journal of Mathematical Physics , 55, 42701001-42701017, 2014.
12. (with C Baesens, R S MacKay) "Abrupt bifurcations in chaotic scattering: view from the anti-integrable limit" , Nonlinearity , 26, 2703-2730, 2013. ([2013 Highlights Collection selected and certified by the Nonlinearity])
13. (with L-C Yeh, I-G Jiang) "Chaotic orbits in a planar three-center problem of slightly negative energy" , International Journal of Bifurcation and Chaos , 22, 123004001-123004016, 2012.
14. (with B Li) "Chaotic and topological properties of β-transformations" , Journal of Mathematical Analysis and Applications , 383, 585-596, 2011.
15. (with T Kawahira, H-L Li, J-M Yuan) "Family of invariant Cantor sets as orbits of differential equations. II: Julia sets" , International Journal of Bifurcation and Chaos , 21, 77-99, 2011.
16. "Family of Julia sets as orbits of differential equations" , RIMS Kokyuroku , 1699, 1-12, 2010.
17. "On topological entropy of billiard tables with small inner scatterers" , Advances in Mathematics , 224, 432-460, 2010.
18. (with F Zhang, Z Chen) "Clique-inserted-graphs and spectral dynamics of clique-inserting" , Journal of Mathematical Analysis and Applications , 349, 211-225, 2009.
19. "Family of invariant Cantor sets as orbits of differential equations" , International Journal of Bifurcation and Chaos , 18 (7), 1825-1843, 2008.
20. "Anti-integrability for the logistic maps" , Chinese Annals of Mathematics B , 28, 219-224, 2007.
21. "Shift automorphisms for tent map: an algebraic proof" , Far East Journal of Dynamical Systems , 8, 81-86, 2006.
22. "Smale horseshoe via the anti-integrability" , Chaos, Solitons and Fractals , 28, 377-385, 2006.
23. "Bernoulli shift for second order recurrence relations near the anti-integrable limit" , Discrete and Continuous Dynamical Systems B , 5, 587-598, 2005.
24. "Anti-integrability in scattering billiards" , Dynamical Systems , 19, 145-159, 2004.
25. "Multibump trajectories continued from the anti-integrable limit for Lagrangian systems" , Regular & Chaotic Dynamics , 8, 243-257, 2003.
26. "Anti-integrability in Lagrangian Systems" , PhD Thesis, Univ of Cambridge , 2002.
27. "Flow Instability in a Cylinder with Counter-Rotating Top and Bottom" , MSc Thesis, National Taiwan Univ , 1993.