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We show that a simply parabolic Polya-Szeg\\\"o inner function admits forward and backward quotient half-cylinders, which allows one to enrich its dynamics with a Lavaurs map.\n  To proceed, we restrict our attention to simply parabolic inner functions with finite Lyapunov exponent: $\\int_{\\mathbb{R}} \\log |F'| d\\ell < \\infty$. We define a geodesic flow on the Riemann surface lamination associated to the Lavaurs semigroup and show that"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.19260","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-17T16:37:42Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"e74f0d25d881e555ffacac7adce024a3b355e7f52d8e9443b94f7875188e7081","abstract_canon_sha256":"353225071de5e293925aeb84fa01c89938fc667b1db83e7ae78bb51691864dd0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:09.089494Z","signature_b64":"6eMuekgzB6D575V4QgLXMiKcDdbpHt7UqcIoXaZLDgPLRh78d690v77FJuFFw/4OtgjuGhHflvhLLHIbrdM3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a715953031aee39300f9c6e790267d386752790fbd8a00153cc76011153a2af","last_reissued_at":"2026-06-19T16:12:09.089128Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:09.089128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of simply parabolic inner functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Oleg Ivrii","submitted_at":"2026-06-17T16:37:42Z","abstract_excerpt":"We study the dynamics of Polya-Szeg\\\"o inner functions and discuss some of their basic properties such as equivalent conditions for simple and double parabolicity. 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