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This article is cited in 2 scientific papers (total in 2 papers)
Complicated behavior in cubic Hénon maps
S. Anastassiou Center of Research and Applications of Nonlinear Systems,
Department of Mathematics, University of Patras, Rion, Greece
Abstract:
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.
Received: 12.11.2020 Revised: 12.11.2020
Citation:
S. Anastassiou, “Complicated behavior in cubic Hénon maps”, TMF, 207:2 (2021), 202–209; Theoret. and Math. Phys., 207:2 (2021), 572–578
Linking options:
https://www.mathnet.ru/eng/tmf10007https://doi.org/10.4213/tmf10007 https://www.mathnet.ru/eng/tmf/v207/i2/p202
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Abstract page: | 185 | Full-text PDF : | 43 | References: | 57 | First page: | 8 |
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