Invariant Curves and Focal Points in a Lyness Iterative Process

@article{Gardini2003InvariantCA,
  title={Invariant Curves and Focal Points in a Lyness Iterative Process},
  author={Laura Gardini and Gian Italo Bischi and Christian Mira},
  journal={I. J. Bifurcation and Chaos},
  year={2003},
  volume={13},
  pages={1841-1852}
}
We investigate the properties of recurrence of the type xn+1 = (a+ ∑k−2 i=0 xn−i)/xn−(k−1), known as Lyness iterations from [Lyness, 1942, 1945, 1961] and recently analyzed by several authors in the case a > 0, see e.g. [Kocic et al., 1993; Csornyei & Laczkovich, 2000]. We reconsider Lyness recurrences at the light of some recent results on iterated maps with denominator, given in [Bischi et al., 1999a], where new kinds of singularities, such as focal points and prefocal curves, have been… CONTINUE READING

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