Anosov diffeomorphism with a horseshoe that attracts almost any point

Name: Work Video:
Duration: 3 min 30 s
Description: We present an example of a $ C^1 $ Anosov diffeomorphism of a two-torus with a physical measure such that its basin has full Lebesgue measure and its support is a horseshoe of zero measure.
Christian Bonatti; Stanislav Minkov; Alexey Okunev; Ivan Shilin
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Mathématiques de Bourgogne [Dijon] (Université de Bourgogne - 9, avenue Alain Savary - B.P. 47 870 - 21078 Dijon Cedex - France)', 'institution_ids': ['https://openalex.org/I4210112333', 'https://openalex.org/I177064439', 'https://openalex.org/I4210166017']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5110347560', 'display_name': 'Stanislav Minkov', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I4210147154', 'display_name': 'Institute of Electronic Control Machines', 'ror': 'https://ror.org/03sxe4z39', 'country_code': 'RU', 'type': 'facility', 'lineage': ['https://openalex.org/I4210147154']}], 'countries': ['RU'], 'is_corresponding': False, 'raw_author_name': 'Stanislav Minkov', 'raw_affiliation_strings': ['INEUM - Institute of Electronic Control Machines (Russie)'], 'affiliations': [{'raw_affiliation_string': 'INEUM - Institute of Electronic Control Machines (Russie)', 'institution_ids': ['https://openalex.org/I4210147154']}]}, 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