Interior periodic points of a Lotka–Volterra map

Abstract

Given the plane triangle and the transformation , we prove the existence of interior periodic points of periods . One of the periodic orbits of period 6 is given explicitly. We also prove that for any lower periodic saddle point, there is an interior periodic point with the same itinerary (with respect to the natural decomposition of Δ given by the vertical middle line).

Keywords:

• periodic point
• Jacobi matrix
• saddle fixed point
• itinerary
• Brouwer theorem

2000 Mathematics Subject Classification::

• 37B99
• 37E15

Acknowledgement

The work was supported by the Slovak grant agency VEGA, grants 1/0855/08 and 1/0828/10 and partially also by the Agency of the Slovak Ministry of Education for the Structural Funds of the EU, under project ITMS:26220120007.