https://hal.archives-ouvertes.fr/hal-01139840Zeng, JinsongJinsongZengLAREMA - Laboratoire Angevin de Recherche en Mathématiques - UA - Université d'Angers - CNRS - Centre National de la Recherche ScientifiqueCRITERION FOR RAYS LANDING TOGETHERHAL CCSD2015[MATH] Mathematics [math][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]zeng, jinsong2015-04-07 11:03:102021-10-20 03:18:472015-04-07 15:42:43enPreprints, Working Papers, ...application/pdf1Let f be a polynomial with degree ≥ 2 and the Julia set J f locally connected. We give a partition of complex plane C and show that, if z, z in J f have the same itinerary respect to the partition, then either z = z or both of them lie in the boundary of a Fatou component U , which is eventually iterated to a siegel disk. As an application, we prove the monotonicity of core entropy for the quadratic polynomial family {fc = z 2 + c : fc has no Siegel disks and J fc is locally connected }.