# Averaging method for differential equations perturbed by dynamical systems

ESAIM: Probability and Statistics (2010)

- Volume: 6, page 33-88
- ISSN: 1292-8100

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topPène, Françoise. "Averaging method for differential equations perturbed by dynamical systems." ESAIM: Probability and Statistics 6 (2010): 33-88. <http://eudml.org/doc/104296>.

@article{Pène2010,

abstract = {
In this paper, we are interested in the asymptotical behavior
of the error between the solution of a differential equation
perturbed by a flow (or by a transformation) and the solution
of the associated averaged differential equation.
The main part of this redaction is devoted to the ascertainment
of results of convergence in distribution analogous to those
obtained in [10] and [11]. As in [11], we shall use a representation
by a suspension flow over a dynamical system. Here, we make an
assumption of multiple decorrelation in terms of this dynamical
system. We show how this property can be verified for ergodic
algebraic toral automorphisms and point out the fact that, for
two-dimensional dispersive billiards, it is a consequence of
the method developed in [18]. Moreover, the singular case of
a degenerated limit distribution is also considered.
},

author = {Pène, Françoise},

journal = {ESAIM: Probability and Statistics},

keywords = {Dynamical system; hyperbolicity; billiard; suspension flow;
limit theorem; averaging method; perturbation; differential equation.; exponential decay of correlations; limit theorem; toral automorphism; Sinai billiards},

language = {eng},

month = {3},

pages = {33-88},

publisher = {EDP Sciences},

title = {Averaging method for differential equations perturbed by dynamical systems},

url = {http://eudml.org/doc/104296},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Pène, Françoise

TI - Averaging method for differential equations perturbed by dynamical systems

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 6

SP - 33

EP - 88

AB -
In this paper, we are interested in the asymptotical behavior
of the error between the solution of a differential equation
perturbed by a flow (or by a transformation) and the solution
of the associated averaged differential equation.
The main part of this redaction is devoted to the ascertainment
of results of convergence in distribution analogous to those
obtained in [10] and [11]. As in [11], we shall use a representation
by a suspension flow over a dynamical system. Here, we make an
assumption of multiple decorrelation in terms of this dynamical
system. We show how this property can be verified for ergodic
algebraic toral automorphisms and point out the fact that, for
two-dimensional dispersive billiards, it is a consequence of
the method developed in [18]. Moreover, the singular case of
a degenerated limit distribution is also considered.

LA - eng

KW - Dynamical system; hyperbolicity; billiard; suspension flow;
limit theorem; averaging method; perturbation; differential equation.; exponential decay of correlations; limit theorem; toral automorphism; Sinai billiards

UR - http://eudml.org/doc/104296

ER -

## References

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