Short desciption
This proposal concerns the topological structure of strange attractors of Hénon type, which emerge universally in chaotic dynamics, for example, in generic unfoldings of homoclinic bifurcations. The standard example are the Hénon attractors themselves, but in its most transparent, linearised form, they are produced by the Lozi map. Despite its widespread appearance in chaotic dynamics, the topological structure of Hénon-like attractors is poorly understood. This proposal suggest to use techniques from unimodal inverse limit spaces (UILs), and specifically the classification methods that led to the solution of the Ingram conjecture, to explore the substructures and possible classification of Hénon-like attractors. This will be combined with symbolic and graphic techniques to display Hénon-attractors and their substructure on small scale.

Workshop
Project funds were used to fund the Workshop "Dynamical systems and continuum theory", June 29-July 3 2015, at the University of Vienna, organized by Jan Boroński, Henk Bruin and Sonja Štimac. Apart from 8 invited talks, there were three minicourses. Click for the program

Publications completed or initiated in this project

• Henk Bruin and Sonja Štimac
  Fibonacci-like unimodal inverse limit spaces and the core Ingram conjecture,
  [.pdf]. Topological Methods in Nonlinear Analysis (TMNA) 47 (2016), 147--185. DOI: 10.12775/TMNA.2016.001
  Arxiv: 1305.4621
• (with Ana Anušić and Jernej Činč) The Core Ingram Conjecture for non-recurrent critical points [.pdf] Fund. Math. 241 (2018), no. 3, 209-235.
• Jozef Bobok and Henk Bruin
  Constant slope maps and the Vere-Jones classification.
  Preprint 2016 [.pdf]. Entropy 18(6) , 234, 2016. DOI:10.3390/e18060234
  Arxiv: 1602.06905
• (with Ana Anušić and Jernej Činč) Uncountably many planar embeddings of unimodal inverse limit spaces Preprint 2016 [.pdf]. Discrete Contin. Dyn. Syst. 37 (2017), no. 5, 2285-2300.
• (with Sonja Štimac) On isotopy of self-homeomorphisms of quadratic inverse limit spaces Preprint July 217 [.pdf]. arXiv version, Topology Proceedings 52 (2018), 167-177
• (with Ana Anušić and Jernej Činč) Problems on planar embeddings of chainable continua and accessibility. In: Problems in Continuum Theory in Memory of Sam B. Nadler, Jr. Ed. Logan Hoehn, Piotr Minc, Murat Tuncali, Topology Proceedings 52 2018, 283-285 in [pdf] and the Auburn source.
• (with Ana Anušić and Jernej Činč) Planar embeddings of chainable continua Preprint 2018 [.pdf].