SaddleDrop

SaddleDrop: a tool for studying dynamics in ℂ 2 In this expository note, we discuss the mathematics behind the computer program SaddleDrop. Based upon ideas of a group at Cornell University, this program draws parameter space pictures for the complex Henon map. The difficulty of this task is explained as we contrast the well-developed theory of one variable complex dynamics with the two variable Henon case.


References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Baake, Michael; Frank, Natalie Priebe; Grimm, Uwe; Robinson, E. Arthur jun.: Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction (2019)
  2. Garijo, Antonio; Jarque, Xavier: Global dynamics of the real secant method (2019)
  3. Arai, Zin; Ishii, Yutaka: On parameter loci of the Hénon family (2018)
  4. Climenhaga, Vaughn; Pesin, Yakov: Building thermodynamics for non-uniformly hyperbolic maps (2017)
  5. Ishii, Yutaka: Dynamics of polynomial diffeomorphisms of (\mathbbC^2): combinatorial and topological aspects (2017)
  6. Koch, Sarah C.: SaddleDrop: a tool for studying dynamics in (\mathbbC^2) (2010)
  7. Ishii, Yutaka: Hyperbolic polynomial diffeomorphisms of (\mathbbC^2). I: A non-planar map (2008)
  8. Arai, Zin: On hyperbolic plateaus of the Hénon map (2007)
  9. Avrutin, V.; Levi, P.; Schanz, M.; Fundinger, D.; Osipenko, G.: Investigation of dynamical systems using symbolic images: efficient implementation and applications (2006)
  10. Bedford, Eric; Smillie, John: The Hénon family: the complex horseshoe locus and real parameter space (2006)
  11. Hruska, Suzanne L.: Rigorous numerical models for the dynamics of complex Hénon mappings on their chain recurrent sets (2006)
  12. Hruska, Suzanne Lynch: A numerical method for constructing the hyperbolic structure of complex Hénon mappings (2006)
  13. Hruska, Suzanne Lynch: Constructing an expanding metric for dynamical systems in one complex variable (2005)