Algebraic orbits on period-3 window for the logistic map

作者：Fidelis Antonio Joao^*; Martins Luciano Camargo

来源：Nonlinear Dynamics, 2015, 79(2): 1015-1021.

DOI：10.1007/s11071-014-1719-0

• Logistic map
• Algebraic results
• Periodic orbits
• Bifurcation
• Period-3 window

Algebraic stable and unstable orbits are presented for the famous period-3 window of the logistic map . It is exhibited the general polynomial that gives rise to both stable and unstable period-3 orbits. These orbits are shown for three different fixed control parameter values of : at tangent bifurcation (birth), at super-stability and at ending pitchfork bifurcation (death) of the period-3 All orbits are exposed in two different ways: a sum of complex numbers , as proposed by Gordon (Math Mag 69:118-120, 1996), and via Euler's formula . The algebraic expressions of and are given for each value for both stable and unstable orbits, as well as their numerical values and the Lyapunov exponent. It is shown that and are statistical quantities of the orbits.

• 出版日期2015-1