Stochastic Dynamics in Simple Systems

  • M. I. Rabinovich
  • D. I. Trubetskov
Part of the Mathematics and Its Applications (Soviet Series) book series (MASS, volume 50)


Naturally all the phenomena and effects considered in the previous chapters were regular in that the oscillations or waves in the systems or media occurred without fluctuations and did not require any statistical method to describe them. Our experience and intuition indicates that in a dynamic system describable by regular equations, nothing irregular or random or stochastic should occur. So where does the randomness come from if we give an unambiguous algorithm that uniquely defines for concrete initial conditions the system for however long in the future1? Obviously, if the system is very complex and has a large number of degrees of freedom (for example, a gas in a vessel), we know that a deterministic description becomes senseless (though in principle possible), if only because it is impossible to specify the initial coordinates and velocities of all of the, say, 1019, molecules in one cubic centimeter of gas. Moreover, there is no computer that can calculate the trajectories of such a number of particles and account for their collisions.


Phase Space Simple System Strange Attractor Dissipative System Stochastic Dynamic 
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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • M. I. Rabinovich
    • 1
  • D. I. Trubetskov
    • 2
  1. 1.Institute of Applied PhysicsAcademy of Sciences of the USSRGorkyUSSR
  2. 2.Saratov State UniversityUSSR

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