Canards and rakes. (Canards et râteux.) (French) Zbl 0756.39003

Fruchard, Augustin

Ann. Inst. Fourier 42, No. 4, 825-855 (1992).

We study the phenomenon of bifurcation delay in discrete dynamic planar systems. The distinction of one invariant curve for the system reduces the study of this phenomenon to the study of one object. We demonstrate the presence of bifurcation delay in oscillating analytic systems. We present a new phenomenon discovered experimentally which appears for non inversible systems: the invariant curve has a series of exponentially tight poles. We demonstrate this phenomenon on two examples. These examples establish a link between the phenomenon of bifurcation delay and the asymptotic behaviour of special or arithmetic functions.

Reviewer: A.Fruchard

MSC:

39A10	Additive difference equations
93C55	Discrete-time control/observation systems
33C15	Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)

Keywords:

\(q\)-difference equation; hypergeometric confluent function; discrete dynamical system; dynamic bifurcation; discret canard; rake; slow-fast application; non-standard analysis; difference equation

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