{"id":{"repo_id":"east-anglia","oai_identifier":"oai:ueaeprints.uea.ac.uk:57191"},"canonical_url":"https://search.dev.ndltd.org/etd/east-anglia/oai:ueaeprints.uea.ac.uk:57191","repository":{"repo_id":"east-anglia","name":"University of East Anglia","base_url":"https://ueaeprints.uea.ac.uk/cgi/oai2"},"display":{"title":"Arithmetic and dynamical systems","abstract":"In this thesis we look at a number of topics in the area of the interaction between dynamical systems and number theory. We look at two diophantine approximation problems in local �fields of positive characteristic, one a generalisation of the Khintchine{Groshev theorem, another a central limit theorem. We also prove a P�olya{Carlson dichotomy result for a large class of adelicly perturbed rational functions. 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In particular we prove that for a finite set of primes S that the power series f(z) generated by the Fibonacci series with all primes in S removed has a natural boundary.","abstract_has_math":false,"creators":["Royals, Robert"],"institution":"University of East Anglia","degree_name":"phd","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-12","date_published":"2015-12","updated_at":"2026-07-24T02:12:13Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Royals, Robert"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-12"]},{"key":"dc:date.issued","label":"Date","values":["2015-12"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of East Anglia"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://ueaeprints.uea.ac.uk/id/eprint/57191/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["phd"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://ueaeprints.uea.ac.uk/id/eprint/57191/1/thesis-robert-royals.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we look at a number of topics in the area of the interaction between dynamical systems and number theory. We look at two diophantine approximation problems in local �fields of positive characteristic, one a generalisation of the Khintchine{Groshev theorem, another a central limit theorem. We also prove a P�olya{Carlson dichotomy result for a large class of adelicly perturbed rational functions. In particular we prove that for a finite set of primes S that the power series f(z) generated by the Fibonacci series with all primes in S removed has a natural boundary."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Arithmetic and dynamical systems"]}]}],"canonical_facts":{"dc:creator":["Royals, Robert"],"dc:date":["2015-12"],"dc:date.issued":["2015-12"],"dc:description.abstract":["In this thesis we look at a number of topics in the area of the interaction between dynamical systems and number theory. We look at two diophantine approximation problems in local �fields of positive characteristic, one a generalisation of the Khintchine{Groshev theorem, another a central limit theorem. We also prove a P�olya{Carlson dichotomy result for a large class of adelicly perturbed rational functions. In particular we prove that for a finite set of primes S that the power series f(z) generated by the Fibonacci series with all primes in S removed has a natural boundary."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://ueaeprints.uea.ac.uk/id/eprint/57191/1/thesis-robert-royals.pdf"],"dc:language":["en"],"dc:publisher.department":["School of Mathematics"],"dc:publisher.institution":["University of East Anglia"],"dc:relation.isreferencedby":["https://ueaeprints.uea.ac.uk/id/eprint/57191/"],"dc:title":["Arithmetic and dynamical systems"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T02:12:13Z"}