Period four stability and multistability domains for the Hénon map

Antônio Endler and Jason A.C. Gallas

Physica A: Statistical Mechanics and its Applications, 2001, vol. 295, issue 1, 285-290

Abstract: We report the exact analytical expression of the surface W4(a,b;λ)=0 defining stability domains for period-4 motions in the Hénon map, valid for arbitrary eigenvalues λ and parameters a and b. For λ=+1 (fold bifurcations) the expression reproduces all previous results and gives a new one. For λ=−1 (flip bifurcations) it gives analytically the missing boundary needed for the rigorous delimitation of all period-4 stability domains and for the investigation of the arithmetic nature of parameters and trajectories.

Keywords: Nonlinear dynamics; Bifurcation loci; Singularities of maps; Reciprocal equations (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:295:y:2001:i:1:p:285-290

DOI: 10.1016/S0378-4371(01)00089-9

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