{'fraction_non_alphanumeric': 0.010443864229765013, 'fraction_numerical': 0.0, 'mean_word_length': 4.907692307692308, '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}}
Transformation to Lienard form

We show that certain two-dimensional differential systems can be transformed to a system of Liénard type. This enables known criteria for the existence of a centre for Liénard systems to be exploited, so extending the range of techniques which are available for proving that conditions which are known to be necessary for a centre are also sufficient.