Regular and Chaotic Dynamics

, Volume 12, Issue 5, pp 490–501 | Cite as

On a separating solution of a recurrent equation

  • Ya. G. Sinai
150th Anniversary of A. M. Lyapunov


We consider the recurrent equation
$$\Lambda _p = \frac{1}{{p - 1}}\sum\limits_{p_1 = 1}^{p - 1} f \left( {\frac{{p_1 }}{p}} \right)\Lambda _{p_1 } \cdot \Lambda _{p - p_1 } $$
. which depends on the initial condition Λ1 = x. Under some conditions on f we show that there exists the value of x for which Λp tends to a constant as p tends to infinity.

Key words

separating solution recurrent equation 

MSC2000 numbers

47A35 37A60 


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  1. 1.
    Li, Dong and Sinai, Ya.G., Blow Ups of Complex Solutions of the 3-Dimensional Navier-Stokes System and Renormalization Group Method, submitted for publication in J. Europ. Math. Soc..Google Scholar
  2. 2.
    Li, Dong, On a Non-linear Recurrent Equation, accepted for publication in the Journal of Stat. Physics.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2007

Authors and Affiliations

  1. 1.Department of MathematicsPennsylvania State UniversityUniversity ParkRussia
  2. 2.Landau Institute of Theoretical PhysicsRussian Academy of SciencesRussia

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