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On polynomial forms of nonlinear functional differential equations

  • * Corresponding author: Olivier Hénot

    * Corresponding author: Olivier Hénot
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  • In this paper we study nonlinear autonomous retarded functional differential equations; that is, functional equations where the time derivative may depend on the past values of the variables. When the nonlinearities in such equations are comprised of elementary functions, we give a constructive proof of the existence of an embedding of the original coordinates yielding a polynomial differential equation. This embedding is a topological conjugacy between the semi-flow of the original differential equation and the semi-flow of the auxiliary polynomial differential equation. Further dynamical features are investigated; notably, for an equilibrium or a periodic orbit and its embedded counterpart, the stable and unstable eigenvalues have the same algebraic and geometric multiplicity.

    Mathematics Subject Classification: Primary: 34Kxx, 34K17, 34K12, 34K20, 37C25; Secondary: 37C86.


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