{'fraction_non_alphanumeric': 0.02737226277372263, 'fraction_numerical': 0.03102189781021898, 'mean_word_length': 4.71875, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
SELF-INDEXING ENERGY FUNCTION FOR MORSE–SMALE

The paper is devoted to finding conditions for the existence of a self-indexing energy function for Morse–Smale diffeomorphisms on a 3-manifold M. These conditions involve how the stable and unstable manifolds of saddle points are embedded in the ambient manifold. We also show that the existence of a self-indexing energy function is equivalent to the existence of a Heegaard splitting of M of a special type with respect to the considered diffeomorphism. 2000 Math. Subj. Class. 37B25, 37D15, 57M30.