{"id":"https://openalex.org/W7215128772","doi":"https://doi.org/10.48550/arxiv.2609.39454","title":"Thermodynamic Formalism on SRB Measures of Compact Convex Projective manifolds, Geometry and Counting","display_name":"Thermodynamic Formalism on SRB Measures of Compact Convex Projective manifolds, Geometry and Counting","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7215128772","doi":"https://doi.org/10.48550/arxiv.2609.39454"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.39454","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39454","pdf_url":"https://arxiv.org/pdf/2609.39454","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.39454","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070965544","display_name":"Patrick Foulon","orcid":"https://orcid.org/0009-0002-7453-8738","observed_orcids":["https://orcid.org/0009-0002-7453-8738"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Foulon, Patrick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5154187867","display_name":"Inkang Kim","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kim, Inkang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/thermodynamic-formalism","display_name":"thermodynamic formalism","score":0.8259999752044678},{"id":"https://openalex.org/keywords/srb-measures","display_name":"SRB measures","score":0.8899999856948853},{"id":"https://openalex.org/keywords/induced-representations","display_name":"induced representations","score":0.718999981880188},{"id":"https://openalex.org/keywords/fundamental-group","display_name":"fundamental group","score":0.75}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6920999884605408},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.6858999729156494},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6477000117301941},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6265000104904175},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.536899983882904},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.510200023651123},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5005999803543091},{"id":"https://openalex.org/C2988735580","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic flow","level":3,"score":0.477400004863739},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.4697999954223633},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.4359999895095825},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3813999891281128},{"id":"https://openalex.org/C177846678","wikidata":"https://www.wikidata.org/wiki/Q1501864","display_name":"Projective test","level":2,"score":0.37700000405311584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37380000948905945},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3325999975204468},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.31850001215934753},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.2971000075340271},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C176021007","wikidata":"https://www.wikidata.org/wiki/Q7249466","display_name":"Projective differential geometry","level":5,"score":0.26739999651908875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.39454","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39454","pdf_url":"https://arxiv.org/pdf/2609.39454","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.39454","doi":"https://doi.org/10.48550/arxiv.2609.39454","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.39454","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.39454","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.39454","pdf_url":"https://arxiv.org/pdf/2609.39454","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215128772.pdf","grobid_xml":"https://content.openalex.org/works/W7215128772.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4388843819","https://openalex.org/W3159521195","https://openalex.org/W4283466773","https://openalex.org/W1809306841","https://openalex.org/W4287118507","https://openalex.org/W3151601947","https://openalex.org/W2766053306","https://openalex.org/W7098641538","https://openalex.org/W2063577160","https://openalex.org/W3105893233"],"abstract_inverted_index":{"We":[0,14,33],"study":[1],"the":[2,16,30,40,44],"Hilbert":[3],"geodesic":[4],"flow":[5,23],"on":[6],"a":[7,26],"closed":[8],"convex":[9],"real":[10],"projective":[11],"$n$-dimensional":[12],"manifold.":[13],"use":[15],"thermodynamic":[17],"formalism":[18],"for":[19,39],"this":[20],"dissipative":[21],"Anosov":[22],"to":[24],"obtain":[25],"geometric":[27],"description":[28],"of":[29,43],"SRB":[31],"measure.":[32],"also":[34],"deduce":[35],"new":[36],"counting":[37],"properties":[38],"induced":[41],"representations":[42],"fundamental":[45],"groups":[46],"in":[47],"$SL(n+1,":[48],"\\R)$.":[49]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-02T00:00:00"}
