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Academic Staff

Chen, Yi-Chiuan

Chen, Yi-Chiuan

Associate Research Fellow

Research Fields: Dynamical Systems

Email : ycchen@math.sinica.edu.tw

Extension : 630

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

  • PhD in Applied Mathematics and Theoretical Physics, University of Cambridge, 2002
  • Certificate of Advanced Study in Mathematics (Part III), DAMTP, University of Cambridge, 1997
  • MSc in Physics, National Taiwan University, 1993
  • BSc in Physics, National Central University, 1991

  • Associate Research Fellow Institute of Mathematics, Academia Sinica 2013 - Present
  • Adjunct Assistant Professor Department of Applied Mathematics, National Chiao Tung Univ, Taiwan 2010/8 - 2011/7
  • 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
  • Associate Editor International Journal of Bifurcation and Chaos 2012 - Present
  • Curator Scholarpedia-the free peer reviewed encyclopedia 2007/8 - Present

  • "Persistence of hyperbolic invariant sets for shift-like diffeomorphisms", (In progress), 202X
  • (with Z Arai) "More on the concept of anti-integrability for Hénon maps", Preprint, 2024
  • "On a question of J.D. Meiss concerning anti-integrability for three-dimensional quadratic diffeomorphisms", arXiv:2402.10536, 2024
  • (with T Kawahira) "From hyperbolic to parabolic parameters along internal rays", Transactions of the American Mathematical Society, 2023, DOI: https://doi.org/10.1090/tran/9080
  • "Holomorphic shadowing for Hénon maps revisited: an implicit function theorem perspective", arXiv:2203.02970, 2022
  • (with T Kawahira) "From Cantor to semi-hyperbolic parameters along external rays", Transactions of the American Mathematical Society, 372, 7959-7992, 2019, doi.org/10.1090/tran/7839
  • "Transitions and anti-integrable limits for multi-hole Sturmian systems and Denjoy counterexamples", Transactions of Mathematics and Its Applications, 3, 0-29, 2019
  • (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
  • "A proof of Devaney-Nitecki region for the Hénon mapping using the anti-integrable limit", Advances in Dynamical Systems and Applications, 13, 33-43, 2018
  • (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
  • (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
  • "Abrupt bifurcation, chaotic scattering, and anti-integrable limit", RIMS Kokyuroku, 1901, 47-54, 2014
  • (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
  • (with C Baesens, R S MacKay) "Abrupt bifurcations in chaotic scattering: view from the anti-integrable limit", Nonlinearity, 26, 2703-2730, 2013
  • (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
  • (with B Li) "Chaotic and topological properties of β-transformations", Journal of Mathematical Analysis and Applications, 383, 585-596, 2011
  • (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
  • "Family of Julia sets as orbits of differential equations", RIMS Kokyuroku, 1699, 1-12, 2010
  • "On topological entropy of billiard tables with small inner scatterers", Advances in Mathematics, 224, 432-460, 2010
  • (with F Zhang, Z Chen) "Clique-inserted-graphs and spectral dynamics of clique-inserting", Journal of Mathematical Analysis and Applications, 349, 211-225, 2009
  • "Family of invariant Cantor sets as orbits of differential equations", International Journal of Bifurcation and Chaos, 18 (7), 1825-1843, 2008
  • "Anti-integrability for the logistic maps", Chinese Annals of Mathematics B, 28, 219-224, 2007
  • "Shift automorphisms for tent map: an algebraic proof", Far East Journal of Dynamical Systems, 8, 81-86, 2006
  • "Smale horseshoe via the anti-integrability", Chaos, Solitons and Fractals, 28, 377-385, 2006
  • "Bernoulli shift for second order recurrence relations near the anti-integrable limit", Discrete and Continuous Dynamical Systems B, 5, 587-598, 2005
  • "Anti-integrability in scattering billiards", Dynamical Systems, 19, 145-159, 2004
  • "Multibump trajectories continued from the anti-integrable limit for Lagrangian systems", Regular & Chaotic Dynamics, 8, 243-257, 2003
  • "Anti-integrability in Lagrangian Systems", PhD Thesis, Univ of Cambridge , 2002
  • "Flow Instability in a Cylinder with Counter-Rotating Top and Bottom", MSc Thesis, National Taiwan Univ, 1993
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