Math Problem Statement
let g(x)=4x(1-x). prove that for each positive integer k there is an orbit of period-k
Solution
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Math Problem Analysis
Mathematical Concepts
Dynamical Systems
Periodic Orbits
Chaos Theory
Logistic Map
Formulas
g(x) = 4x(1 - x)
g^k(x_0) = x_0 for an orbit of period k
Theorems
Sharkovskii's Theorem
Suitable Grade Level
Undergraduate to Graduate
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