Snap-back repellers in non-smooth functions

    2010, Volume 15, Numbers 2-3, pp.  237-245

    Author(s): Gardini L., Tramontana F.

    In this work we consider the homoclinic bifurcations of expanding periodic points. After Marotto, when homoclinic orbits to expanding periodic points exist, the points are called snap-back-repellers. Several proofs of the existence of chaotic sets associated with such homoclinic orbits have been given in the last three decades. Here we propose a more general formulation of Marotto’s theorem, relaxing the assumption of smoothness, considering a generic piecewise smooth function, continuous or discontinuous. An example with a two-dimensional smooth map is given and one with a two-dimensional piecewise linear discontinuous map.
    Keywords: snap back repellers, homoclinic orbits in noninvertible maps, orbits homoclinic to expanding points
    Citation: Gardini L., Tramontana F., Snap-back repellers in non-smooth functions, Regular and Chaotic Dynamics, 2010, Volume 15, Numbers 2-3, pp. 237-245

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