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Kumar","submitted_at":"2014-06-10T07:54:49Z","abstract_excerpt":"We consider two families of functions $\\mathcal{F}=\\{f_{{\\la},{\\xi}}(z)= e^{-z+\\la}+\\xi: \\la,\\,\\xi\\in\\C, \\RE{\\la}<0, \\RE\\xi\\geq 1\\}$ and $\\mathcal{F}'=\\{f_{{\\mu},{\\ze}}(z)= e^{z+\\mu}+\\ze: \\mu,\\,\\ze\\in\\C, \\RE{\\mu}<0, \\RE\\ze\\leq-1\\}$ and investigate the escaping sets of members of the family $\\mathcal F$ and $\\mathcal F'.$ We also consider the dynamics of composite entire functions and provide conditions for equality of escaping sets of two transcendental entire functions."},"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":"1406.2453","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-10T07:54:49Z","cross_cats_sorted":[],"title_canon_sha256":"c8ae97e738a354aa7c50a086e907c50d405c5c1519055c4304994b834c20d124","abstract_canon_sha256":"462d709c62169f2bd9559a80907cdc256773d1c1ac05fd6edc671b58e77b99d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:11.835377Z","signature_b64":"Aij6SyxemgNXyKWn/8gJLmIsg2+BEqISYdfTKXHd69aGs5pQIFfHPlfi/eY8sz5BtJNhqzxNOlzzfjz41GUVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a68c092c4e3dc2a93b9a7a0f06012b9dfc1b49b892e7357a1cdc94de671c86f8","last_reissued_at":"2026-05-18T01:31:11.834887Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:11.834887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On escaping sets of some families of entire functions and dynamics of composite entire functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"D. 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