{'fraction_non_alphanumeric': 0.018518518518518517, 'fraction_numerical': 0.0, 'mean_word_length': 5.011111111111111, '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}}
Dynamics of maps with nilpotent Jacobians

The Discrete Markus-Yamabe Conjecture (also known as the LaSalle Conjecture) imposed conditions on the Jacobian eigenvalues of a map in the hope of ensuring global attractivity of the fixed point. This paper pushes such assumptions to their extreme; the Jacobian is assumed to be nilpotent at all points. The dynamics of such maps is studied and diverse behaviour is observed, from the quick collapse of points to a globally attractive fixed point, to maps with self-intersecting invariant curves.