ΣΥΜΒΟΛΗ ΣΤΗ ΘΕΩΡΙΑ ΤΩΝ D+- ΕΥΣΤΑΘΩΝ ΔΥΝΑΜΙΚΩΝ ΣΥΣΤΗΜΑΤΩΝ ΣΕ ΔΙΔΙΑΣΤΑΤΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ

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.

Grantor dc:publisher

National and Kapodistrian University of Athens

Year dc:date

1986

Authors dc:creator

• Athanasopoulou, Konstantinos
• Αθανασόπουλος, Κωνσταντίνος

• 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

Language dc:language

gre

Identifier

10.12681/eadd/0153

OAI identifier oai:identifier

oai:10442/0153