Convergence analysis of Davidchack and Lai's algorithm for finding periodic orbits

We rigorously study a recent algorithm due to Davidchack and Lai (DL) [Davi dchack RL, Lai Y-C. Phys Rev E 1999;60(5):6172-5] for efficiently locating complete sets of hyperbolic periodic orbits for chaotic maps. We give theor ems concerning sufficient conditions on convergence and also describing var iable sized basins of attraction of initial seeds, thus pointing out a part icularly attractive feature of the DL-algorithm. We also point out the true role of involutary matrices which is different from that implied by Schmel cher and Diakonos [Schmelcher P, Diakonos FK. Phys Rev E 1998;57(3):2739-46 ] and propagated by Davidchack and Lai. (C) 2001 Elsevier Science Ltd. All rights reserved.