On a class of strongly contractive quadratic recurrent systems |
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Authors: | D Li |
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Institution: | 1.School of Mathematics,Institute for Advanced Study,Princeton,USA |
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Abstract: | We consider a class of nonlinear recurrent systems of the form \( {\Lambda_p} = \frac{1}{p}\sum\limits_{{p_1} = 1}^{p - 1} {f\left( {\frac{{{p_1}}}{p}} \right){\Lambda_{{p_1}}}{\Lambda_{p - {p_1}}}} \), p > 1, where f is a given function on the interval 0, 1] and Λ1 = x is an adjustable real-valued parameter. Under some suitable assumptions on the function f, we show that there exists an initial value x * for which Λ p = Λ p (x * ) → const as p → ∞. More precise asymptotics of Λ p is also derived. |
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