Geodesic
Complicated behavior in cubic H\'enon maps
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 202-209

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We study a generalized Hénon map in two-dimensional space. We find a region of the phase space where the nonwandering set exists, specify parameter values for which this nonwandering set is hyperbolic, and prove that our map when restricted to a specific invariant subset is topologically conjugate to the Bernoulli three-shift. Coupling two such maps, as a result, we obtain a map in four-dimensional space and show that Bernoulli shifts also exist in this map.
Keywords: cubic Hénon map, Bernoulli shift, hyperbolic dynamics. 
@article{TMF_2021_207_2_a2,
     author = {S. Anastassiou},
     title = {Complicated behavior in cubic {H\'enon} maps},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {202--209},
     publisher = {mathdoc},
     volume = {207},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a2/}
}
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S. Anastassiou. Complicated behavior in cubic H\'enon maps. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 202-209. http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a2/