Advanced search
Publication Cover
Experimental Mathematics Volume 16, 2007 - Issue 2
Submit an article Journal homepage
49
Views
28
CrossRef citations to date
0
Altmetric
Original Article

On Hyperbolic Plateaus of the Hénon Map

Zin Arai Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
Pages 181-188 | Published online: 30 Jan 2011

  • Z. Arai. "On Loops in the Hyperbolic Locus of the Complex Hénon Map." Preprint, 2007.
  • Z. Arai and K. Mischaikow. "Rigorous Computations of Homoclinic Tangencies." SIAM J. Appl. Dyn. Syst. 5 (2006), 280–292.
  • E. Bedford and J. Smillie. "Polynomial Diffeomorphisms of C 2: Currents, Equilibrium Measure and Hyperbolicity." Invent. math. 103 (1991), 69–99.
  • E. Bedford and J. Smillie. "Real Polynomial Diffeomorphisms with Maximal Entropy: Tangencies." Ann. Math. 160 (2004), 1–26.
  • E. Bedford and J. Smillie. "Real Polynomial Diffeomorphisms with Maximal Entropy: II. Small Jacobian." Preprint, 2004.
  • E. Bedford and J. Smillie. "The Hénon Family: The Complex Horseshoe Locus and Real Parameter Values." Contemp. Math. 396 (2006), 21–36.
  • Y. Cao, S. Luzzatto, and I. Rios. "The Boundary of Hyperbolicity for Hénon-like Families." arXiv:math.DS/0502235, 2005.
  • R. C. Churchill, J. Franke. and J. Selgrade. "A Geometric Criterion for Hyperbolicity of Flows." Proc. Amer. Math. Soc. 62 (1977), 137–143.
  • M. J. Davis, R. S. MacKay, and A. Sannami. "Markov Shifts in the Hénon Family." Physica D, 52 (1991), 171–178.
  • M. Dellnitz and O. Junge. "Set Oriented Numerical Methods for Dynamical Systems." In Handbook of Dynamical Systems II, pp. 221–264. Amsterdam: North-Holland, 2002.
  • R. Devaney and Z. Nitecki. "Shift Automorphisms in the Hénon Mapping." Commun. Math. Phys. 67 (1979), 137–146.
  • R. Hagiwara and A. Shudo. "An Algorithm to Prune the Area-Preserving Hénon Map." J. Phys. A: Math. Gen. 37 (2004), 10521–10543.
  • H. El Hamouly and C. Mira. "Lien entre les propriétés d'un endomorphisme de dimension un et celles d'un difféomorphisme de dimension deux." C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), 525–528.
  • S. L. Hruska. "A Numerical Method for Constructing the Hyperbolic Structure of Complex Hénon Mappings." Foundations of Computational Mathematics 6 (2006), 427–455.
  • S. L. Hruska. "Rigorous Numerical Studies of the Dynamics of Polynomial Skew Products of ℂ2." Contemp. Math. 396 (2006), 85–100.
  • K. Mischaikow and M. Mrozek. "The Conley Index Theory." In Handbook of Dynamical Systems II, pp. 393–460. Amsterdam: North-Holland, 2002.
  • C. Robinson. Dynamical Systems; Stability, Symbolic Dynamics, and Chaos, second edition. Boca Raton: CRC Press, 1999.
  • R. J. Sacker and G. R. Sell. "Existence of Dichotomies and Invariant Splitting for Linear Differential Systems I." J. Differential Equations 27 (1974), 429–458.
  • A. Sannami. "A Topological Classification of the Periodic Orbits of the Hénon Family." Japan J. Appl. Math. 6 (1989), 291–300.
  • A. Sannami. "On the Structure of the Parameter Space of the Hénon Map." In Towards the Harnessing of Chaos, pp. 289–303. Amsterdam: Elsevier, 1994.
  • R. Sedgewick. Algorithms. Reading, MA: Addison-Wesley, 1983.
  • D. Sterling, H. R. Dullin, and J. D. Meiss. "Homoclinic Bifurcations for the Hénon Map." Physica D 134 (1999), 153–184.
  • A. Szymczak. "A Combinatorial Procedure for Finding Isolating Neighbourhoods and Index Pairs." Proc. Roy. Soc. Edinburgh Sect. A 127 (1997), 1075–1088.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.