{"id":{"repo_id":"greece","oai_identifier":"oai:10442/0153"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/0153","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΣΥΜΒΟΛΗ ΣΤΗ ΘΕΩΡΙΑ ΤΩΝ D+- ΕΥΣΤΑΘΩΝ ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ ΣΕ ΔΙΔΙΑΣΤΑΤΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ","abstract":"WE ARE CONCERNED WITH THE GLOBAL QUALITIVE BEHAVIOR OF D+-STABLE (OR CHARACTERISTIC O+) DYNAMICAL SYSTEMS ON 2-MANIFOLDS, IN CONNECTION WITH THE TOPOLOGICALSTRUCTURE OF THE UNDERLYING PHASE SPACES. FIRST WE PROVE THAT A STABLE COMPACT MINIMAL SET OF A (NOT NECESSARILY D+ - STABLE) DYNAMICAL SYSTEM ON A 2-MANIFOLD IS TRIVIAL. USING THIS RESULT WE PROVE THAT THERE ARE ONLY SEVEN 2-MANIFOLDS SUPPORTING D+ - STABLE DYNAMICAL SYSTEMS WITH AT LEAST ONE PERIODIC ORBIT. FROM THIS WE DEDUCE THAT THERE ARE ONLY FOUR COMPACT 2-MANIFOLDS WHICH CAN SUPPORT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL SYSTEM. ON THE CONTRARY, ON EVERY NON-COMPACT 2-MANIFOLD WE CONSTRUCT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL SYSTEM. FINALLY, USING ALL THE PREVIOUSLY OBTAINED RESULTS WE PROVE THAT EVERY (CONTINUOUS) D+ - STABLE DYNAMICAL SYSTEM ON A 2- MANIFOLD IS TOPOLOGICALLY EQUIVALENT TO A SMOOTH (I.E. E -DIFFERENTIABLE) D+ - STABLE DYNAMICAL SYSTEM.","abstract_html":"WE ARE CONCERNED WITH THE GLOBAL QUALITIVE BEHAVIOR OF D+-STABLE (OR CHARACTERISTIC O+) DYNAMICAL SYSTEMS ON 2-MANIFOLDS, IN CONNECTION WITH THE TOPOLOGICALSTRUCTURE OF THE UNDERLYING PHASE SPACES. FIRST WE PROVE THAT A STABLE COMPACT MINIMAL SET OF A (NOT NECESSARILY D+ - STABLE) DYNAMICAL SYSTEM ON A 2-MANIFOLD IS TRIVIAL. USING THIS RESULT WE PROVE THAT THERE ARE ONLY SEVEN 2-MANIFOLDS SUPPORTING D+ - STABLE DYNAMICAL SYSTEMS WITH AT LEAST ONE PERIODIC ORBIT. FROM THIS WE DEDUCE THAT THERE ARE ONLY FOUR COMPACT 2-MANIFOLDS WHICH CAN SUPPORT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL SYSTEM. ON THE CONTRARY, ON EVERY NON-COMPACT 2-MANIFOLD WE CONSTRUCT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL SYSTEM. FINALLY, USING ALL THE PREVIOUSLY OBTAINED RESULTS WE PROVE THAT EVERY (CONTINUOUS) D+ - STABLE DYNAMICAL SYSTEM ON A 2- MANIFOLD IS TOPOLOGICALLY EQUIVALENT TO A SMOOTH (I.E. E -DIFFERENTIABLE) D+ - STABLE DYNAMICAL SYSTEM.","abstract_has_math":false,"creators":["Athanasopoulou, Konstantinos","Αθανασόπουλος, Κωνσταντίνος"],"institution":"National and Kapodistrian University of Athens","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1986,"date_issued":"1986","date_published":"1986","updated_at":"2026-07-24T02:24:59Z","subjects":["2-ΠΟΛΛΑΠΛΟΤΗΤΑ","D -ΕΥΣΤΑΘΕΙΑ {ΧΑΡΑΚΤΗΡΙΣΤΙΚΗ Ο }","ΔΥΝΑΜΙΚΟ ΣΥΣΤΗΜΑ","ΕΛΑΧΙΣΤΟ ΣΥΝΟΛΟ","Ευστάθεια","Λείανση","Μαθηματικά","2-MANIFOLD","D -STABILITY {CHARACTERISTIC O }","Dynamical systems","MINIMAL SET","Smoothing","Stability","Φυσικές Επιστήμες","Natural Sciences","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0153"],"render_values":[{"text":"10.12681/eadd/0153","href":"https://doi.org/10.12681/eadd/0153","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/0153","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Athanasopoulou, Konstantinos","Αθανασόπουλος, Κωνσταντίνος"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1986"]},{"key":"dc:publisher","label":"Institution","values":["National and Kapodistrian University of Athens","Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["2-ΠΟΛΛΑΠΛΟΤΗΤΑ","D -ΕΥΣΤΑΘΕΙΑ {ΧΑΡΑΚΤΗΡΙΣΤΙΚΗ Ο }","ΔΥΝΑΜΙΚΟ ΣΥΣΤΗΜΑ","ΕΛΑΧΙΣΤΟ ΣΥΝΟΛΟ","Ευστάθεια","Λείανση","Μαθηματικά","2-MANIFOLD","D -STABILITY {CHARACTERISTIC O }","Dynamical systems","MINIMAL SET","Smoothing","Stability","Φυσικές Επιστήμες","Natural Sciences","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0153","http://hdl.handle.net/10442/hedi/0153"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["WE ARE CONCERNED WITH THE GLOBAL QUALITIVE BEHAVIOR OF D+-STABLE (OR CHARACTERISTIC O+) DYNAMICAL SYSTEMS ON 2-MANIFOLDS, IN CONNECTION WITH THE TOPOLOGICALSTRUCTURE OF THE UNDERLYING PHASE SPACES. FIRST WE PROVE THAT A STABLE COMPACT MINIMAL SET OF A (NOT NECESSARILY D+ - STABLE) DYNAMICAL SYSTEM ON A 2-MANIFOLD IS TRIVIAL. USING THIS RESULT WE PROVE THAT THERE ARE ONLY SEVEN 2-MANIFOLDS SUPPORTING D+ - STABLE DYNAMICAL SYSTEMS WITH AT LEAST ONE PERIODIC ORBIT. FROM THIS WE DEDUCE THAT THERE ARE ONLY FOUR COMPACT 2-MANIFOLDS WHICH CAN SUPPORT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL SYSTEM. ON THE CONTRARY, ON EVERY NON-COMPACT 2-MANIFOLD WE CONSTRUCT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL SYSTEM. FINALLY, USING ALL THE PREVIOUSLY OBTAINED RESULTS WE PROVE THAT EVERY (CONTINUOUS) D+ - STABLE DYNAMICAL SYSTEM ON A 2- MANIFOLD IS TOPOLOGICALLY EQUIVALENT TO A SMOOTH (I.E. E -DIFFERENTIABLE) D+ - STABLE DYNAMICAL SYSTEM.","ΜΑΣ ΕΝΔΙΑΦΕΡΕΙ Η ΔΙΑΣΥΝΔΕΣΗ ΤΗΣ ΟΛΙΚΗΣ ΠΟΙΟΤΙΚΗΣ ΣΥΜΠΕΡΙΦΟΡΑΣ ΤΩΝ D+ - ΕΥΣΤΑΘΩΝ(# ΧΑΡΑΚΤΗΡΙΣΤΙΚΗΣ Ο+) ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ ΣΕ 2- ΠΟΛΛΑΠΛΟΤΗΤΕΣ, ΜΕ ΤΗΝ ΤΟΠΟΛΟΓΙΚΗ ΔΟΜΗ ΤΩΝ ΥΠΟΚΕΙΜΕΝΩΝ ΠΟΛΛΑΠΛΟΤΗΤΩΝ. ΣΤΗΝ ΑΡΧΗ ΑΠΟΔΕΙΚΝΥΟΥΜΕ ΟΤΙ ΕΝΑ ΕΥΣΤΑΘΕΣ, ΣΥΜΠΑΓΕΣ ΚΑΙ ΕΛΑΧΙΣΤΟ ΣΥΝΟΛΟ ΕΝΟΣ (ΟΧΙ ΚΑΤ'ΑΝΑΓΚΗ D+ -ΕΥΣΤΑΘΟΥΣ) ΔΥΝΑΜΙΚΟΥ ΣΥΣΤΗΜΑΤΟΣ ΠΑΝΩ ΣΕ ΜΙΑ 2-ΠΟΛΛΑΠΛΟΤΗΤΑ ΕΙΝΑΙ ΤΕΤΡΙΜΕΝΟ. ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΟ ΑΠΟΤΕΛΕΣΜΑ ΑΥΤΟ, ΑΠΟΔΕΙΚΝΥΟΥΜΕ ΟΤΙ ΥΠΑΡΧΟΥΝ ΑΚΡΙΒΩΣ ΕΠΤΑ ΣΤΟΝ ΑΡΙΘΜΟ 2-ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΠΟΥ ΔΕΧΟΝΤΑΙ D+ -ΕΥΣΤΑΘΕΣ ΔΥΝΑΜΙΚΑ ΣΥΣΤΗΜΑΤΑ ΜΕ ΤΟΥΛΑΧΙΣΤΟΝ ΜΙΑ ΠΕΡΙΟΔΙΚΗ ΤΡΟΧΙΑ, ΚΑΙ ΠΕΡΙΓΡΑΦΟΥΜΕ ΤΑ ΣΥΣΤΗΜΑΤΑ ΑΥΤΑ. ΥΠΑΡΧΟΥΝ ΕΠΙΣΗΣ ΜΟΝΟ ΤΕΣΣΕΡΕΙΣ ΣΥΜΠΑΓΕΙΣ 2-ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΠΟΥ ΜΠΟΡΟΥΝ ΝΑ ΔΕΧΘΟΥΝ (ΟΧΙ ΤΕΤΡΙΜΕΝΑ) D+ - ΕΥΣΤΑΘΗ ΔΥΝΑΜΙΚΑ ΣΥΣΤΗΜΑΤΑ. ΑΝΤΙΘΕΤΑ, ΣΕ ΚΑΘΕ ΜΗ-ΣΥΜΠΑΓΗ 2- ΠΟΛΛΑΠΛΟΤΗΤΑ ΚΑΤΑΣΚΕΥΑΖΟΥΜΕΕΝΑ (ΟΧΙ ΤΕΤΡΙΜΕΝΟ) D+ -ΕΥΣΤΑΘΕΣ ΔΥΝΑΜΙΚΟ ΣΥΣΤΗΜΑ. ΤΕΛΟΣ, ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΑ ΠΡΟΗΓΟΥΜΕΝΑ, ΑΠΟΔΕΙΚΝΥΟΥΜΕ ΟΤΙ ΚΑΘΕ (ΣΥΝΕΧΕΣ) D+ -ΕΥΣΤΑΘΕΣ ΔΥΝΑΜΙΚΟ ΣΥΣΤΗΜΑ ΣΕΜΙΑ 2- ΠΟΛΛΑΠΛΟΤΗΤΑ ΕΙΝΑΙ ΤΟΠΟΛΟΓΙΚΑ ΙΣΟΔΥΝΑΜΟ ΜΕ ΕΝΑ E -ΔΙΑΦΟΡΙΣΙΜΟ D+- ΕΥΣΤΑΘΕΣ ΔΥΝΑΜΙΚΟ ΣΥΣΤΗΜΑ."]},{"key":"dc:title","label":"Title","values":["ΣΥΜΒΟΛΗ ΣΤΗ ΘΕΩΡΙΑ ΤΩΝ D+- ΕΥΣΤΑΘΩΝ ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ ΣΕ ΔΙΔΙΑΣΤΑΤΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ","CONTRIBUTION TO THE THEORY OF D+-STABLE DYNAMICAL SYSTEMS ON TWO- DIMENSIONAL MANIFOLDS"]}]}],"canonical_facts":{"dc:creator":["Athanasopoulou, Konstantinos","Αθανασόπουλος, Κωνσταντίνος"],"dc:date":["1986"],"dc:description":["WE ARE CONCERNED WITH THE GLOBAL QUALITIVE BEHAVIOR OF D+-STABLE (OR CHARACTERISTIC O+) DYNAMICAL SYSTEMS ON 2-MANIFOLDS, IN CONNECTION WITH THE TOPOLOGICALSTRUCTURE OF THE UNDERLYING PHASE SPACES. FIRST WE PROVE THAT A STABLE COMPACT MINIMAL SET OF A (NOT NECESSARILY D+ - STABLE) DYNAMICAL SYSTEM ON A 2-MANIFOLD IS TRIVIAL. USING THIS RESULT WE PROVE THAT THERE ARE ONLY SEVEN 2-MANIFOLDS SUPPORTING D+ - STABLE DYNAMICAL SYSTEMS WITH AT LEAST ONE PERIODIC ORBIT. FROM THIS WE DEDUCE THAT THERE ARE ONLY FOUR COMPACT 2-MANIFOLDS WHICH CAN SUPPORT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL SYSTEM. ON THE CONTRARY, ON EVERY NON-COMPACT 2-MANIFOLD WE CONSTRUCT A (NON-TRIVIAL) D+ - STABLE DYNAMICAL SYSTEM. FINALLY, USING ALL THE PREVIOUSLY OBTAINED RESULTS WE PROVE THAT EVERY (CONTINUOUS) D+ - STABLE DYNAMICAL SYSTEM ON A 2- MANIFOLD IS TOPOLOGICALLY EQUIVALENT TO A SMOOTH (I.E. E -DIFFERENTIABLE) D+ - STABLE DYNAMICAL SYSTEM.","ΜΑΣ ΕΝΔΙΑΦΕΡΕΙ Η ΔΙΑΣΥΝΔΕΣΗ ΤΗΣ ΟΛΙΚΗΣ ΠΟΙΟΤΙΚΗΣ ΣΥΜΠΕΡΙΦΟΡΑΣ ΤΩΝ D+ - ΕΥΣΤΑΘΩΝ(# ΧΑΡΑΚΤΗΡΙΣΤΙΚΗΣ Ο+) ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ ΣΕ 2- ΠΟΛΛΑΠΛΟΤΗΤΕΣ, ΜΕ ΤΗΝ ΤΟΠΟΛΟΓΙΚΗ ΔΟΜΗ ΤΩΝ ΥΠΟΚΕΙΜΕΝΩΝ ΠΟΛΛΑΠΛΟΤΗΤΩΝ. ΣΤΗΝ ΑΡΧΗ ΑΠΟΔΕΙΚΝΥΟΥΜΕ ΟΤΙ ΕΝΑ ΕΥΣΤΑΘΕΣ, ΣΥΜΠΑΓΕΣ ΚΑΙ ΕΛΑΧΙΣΤΟ ΣΥΝΟΛΟ ΕΝΟΣ (ΟΧΙ ΚΑΤ'ΑΝΑΓΚΗ D+ -ΕΥΣΤΑΘΟΥΣ) ΔΥΝΑΜΙΚΟΥ ΣΥΣΤΗΜΑΤΟΣ ΠΑΝΩ ΣΕ ΜΙΑ 2-ΠΟΛΛΑΠΛΟΤΗΤΑ ΕΙΝΑΙ ΤΕΤΡΙΜΕΝΟ. ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΟ ΑΠΟΤΕΛΕΣΜΑ ΑΥΤΟ, ΑΠΟΔΕΙΚΝΥΟΥΜΕ ΟΤΙ ΥΠΑΡΧΟΥΝ ΑΚΡΙΒΩΣ ΕΠΤΑ ΣΤΟΝ ΑΡΙΘΜΟ 2-ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΠΟΥ ΔΕΧΟΝΤΑΙ D+ -ΕΥΣΤΑΘΕΣ ΔΥΝΑΜΙΚΑ ΣΥΣΤΗΜΑΤΑ ΜΕ ΤΟΥΛΑΧΙΣΤΟΝ ΜΙΑ ΠΕΡΙΟΔΙΚΗ ΤΡΟΧΙΑ, ΚΑΙ ΠΕΡΙΓΡΑΦΟΥΜΕ ΤΑ ΣΥΣΤΗΜΑΤΑ ΑΥΤΑ. ΥΠΑΡΧΟΥΝ ΕΠΙΣΗΣ ΜΟΝΟ ΤΕΣΣΕΡΕΙΣ ΣΥΜΠΑΓΕΙΣ 2-ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΠΟΥ ΜΠΟΡΟΥΝ ΝΑ ΔΕΧΘΟΥΝ (ΟΧΙ ΤΕΤΡΙΜΕΝΑ) D+ - ΕΥΣΤΑΘΗ ΔΥΝΑΜΙΚΑ ΣΥΣΤΗΜΑΤΑ. ΑΝΤΙΘΕΤΑ, ΣΕ ΚΑΘΕ ΜΗ-ΣΥΜΠΑΓΗ 2- ΠΟΛΛΑΠΛΟΤΗΤΑ ΚΑΤΑΣΚΕΥΑΖΟΥΜΕΕΝΑ (ΟΧΙ ΤΕΤΡΙΜΕΝΟ) D+ -ΕΥΣΤΑΘΕΣ ΔΥΝΑΜΙΚΟ ΣΥΣΤΗΜΑ. ΤΕΛΟΣ, ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΑ ΠΡΟΗΓΟΥΜΕΝΑ, ΑΠΟΔΕΙΚΝΥΟΥΜΕ ΟΤΙ ΚΑΘΕ (ΣΥΝΕΧΕΣ) D+ -ΕΥΣΤΑΘΕΣ ΔΥΝΑΜΙΚΟ ΣΥΣΤΗΜΑ ΣΕΜΙΑ 2- ΠΟΛΛΑΠΛΟΤΗΤΑ ΕΙΝΑΙ ΤΟΠΟΛΟΓΙΚΑ ΙΣΟΔΥΝΑΜΟ ΜΕ ΕΝΑ E -ΔΙΑΦΟΡΙΣΙΜΟ D+- ΕΥΣΤΑΘΕΣ ΔΥΝΑΜΙΚΟ ΣΥΣΤΗΜΑ."],"dc:identifier":["10.12681/eadd/0153","http://hdl.handle.net/10442/hedi/0153"],"dc:language":["gre"],"dc:publisher":["National and Kapodistrian University of Athens","Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)"],"dc:subject":["2-ΠΟΛΛΑΠΛΟΤΗΤΑ","D -ΕΥΣΤΑΘΕΙΑ {ΧΑΡΑΚΤΗΡΙΣΤΙΚΗ Ο }","ΔΥΝΑΜΙΚΟ ΣΥΣΤΗΜΑ","ΕΛΑΧΙΣΤΟ ΣΥΝΟΛΟ","Ευστάθεια","Λείανση","Μαθηματικά","2-MANIFOLD","D -STABILITY {CHARACTERISTIC O }","Dynamical systems","MINIMAL SET","Smoothing","Stability","Φυσικές Επιστήμες","Natural Sciences","Mathematics"],"dc:title":["ΣΥΜΒΟΛΗ ΣΤΗ ΘΕΩΡΙΑ ΤΩΝ D+- ΕΥΣΤΑΘΩΝ ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ ΣΕ ΔΙΔΙΑΣΤΑΤΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ","CONTRIBUTION TO THE THEORY OF D+-STABLE DYNAMICAL SYSTEMS ON TWO- DIMENSIONAL MANIFOLDS"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:59Z"}