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ANALYTICAL AND NUMERICAL METHODS OF CHAOTIC DYNAMICS

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ΑΝΑΛΥΤΙΚΕΣ ΚΑΙ ΑΡΙΘΜΗΤΙΚΕΣ ΜΕΘΟΔΟΙ ΧΑΟΤΙΚΗΣ ΔΥΝΑΜΙΚΗΣ
ANALYTICAL AND NUMERICAL METHODS OF CHAOTIC DYNAMICS
Δρόσος, Λάμπρος
Drossos, Lambros
PhD Thesis
1993
THE MAIN GOAL OF THIS THESIS IS TO DEVELOP AND USE ANALYTICAL AS WELL AS NUMERICAL METHODS STUDYING THE SOLUTIONS OF SYSTEMS OF NON LINEAR O.D.E'S WHICHDESCRIBE DYNAMICAL SYSTEMS OF PHYSICAL INTEREST. THE STUDY OF SYSTEMS PRESERVING A "DENSITY" OR "MEASURE" QUANTITY IN TIME, ESPECIALLY THE STUDY OF PERIOD DOUBLING SENARIO, SHOWS THAT SUCH SYSTEMS HAVE THE SAME PROPERTIES WITH HAMILTONIAN ONES. ALSO THE MEASURE PRESERVATION PROPERTY IS DIRECTLY CONNECTED WITH THE REVERSIBILITY ONE, WHERE REVERSING THE TIME, THE VECTOR FIELD OF THE SYSTEM REVERSES. IN THE STUDY OF NONLINEAR OSCILLATIONS THE ACURATE COMPUTATION, STABILITY ANALYSIS AND BIFURCATION PROPERTIES OF PERIODIC SOLUTIONS,ARE OF PRIMITIVE ROLE. GENERALLY SPEAKING, THE SOLUTIONS (OR ORBITS) OF THESE SYSTEMS ARE COMPUTED BY NUMERICAL EXPLORATION OF THE PHASE SPACE, SO THATTHE INITIAL CONDITIONS OF EVERY ORBIT ARE ACCURATELY COMPUTED. BUT IF AN ORBIT IS UNSTABLE, SUCH AN EXPLORATION FAILS OR HAS A BIG NUMERICAL COST, ESPECIALLY IN THE CASE OF THE HIGH PERIOD ORBITS. HERE THE COMPUTATION OF PERIODIC ORBITS USING FOURIER SERIES EXPANSIONS, COMPUTED SOLVING, WITH REPEATIVE METHODS, THE CORRESPONDING ALGEBRAIC SYSTEM WITH (COMPLEX) COEFFICIENTS OF THE SERIES AS UNKNOWNS, SHOWS WHERE THESE METHODS ARE BETTER OR NOT, COMPAREDWITH THE CLASSICAL METHODS SOLVING ALGEBRAIC SYSTEMS AS WELL AS COMPUTING PERIODIC ORBITS. ALSO THE STABILITY ANALYSIS IS MADE USING THE COEFFICIENT OF FOURIER EXPANSIONS USING HILL'S METHOD OF ANALYSIS. (ABSTRACT TRUNCATED)
Μαθηματικά
Φυσικές Επιστήμες
Chaos
Periodic orbits
PERIOD DOUBLING
CONSERVATIVE SYSTEMS
RIEMANN SURFACES
Bifurcations
Μαθηματικά
Mathematics
SURFACES OF SECTION
Φυσικές Επιστήμες
ΑΠΕΙΡΩΣ ΠΛΕΙΟΤΙΜΕΣ ΛΥΣΕΙΣ (ΑΠΛ)
ΑΝΑΛΥΣΗ ΙΔΙΟΜΟΡΦΙΩΝ
Περιοδικές τροχιές
Αλγεβρικές ιδιομορφίες
SINGULARITY ANALYSIS
ACCUMULATION OF SINGULARITIES
Natural Sciences
ΔΙΑΤΗΡΗΤΙΚΑ ΣΥΣΤΗΜΑΤΑ
Διακλαδώσεις
ΑΝΤΙΣΤΡΕΨΙΜΑ ΣΥΣΤΗΜΑΤΑ
Integrability
ΣΥΣΣΩΡΕΥΣΗ ΙΔΙΟΜΟΡΦΙΩΝ
REPEATITIVECALCULATION METHODS
Ολοκληρωσιμότητα
REVERSIBLE SYSTEMS
ΕΠΙΦΑΝΕΙΕΣ ΤΟΜΩΝ
FOURIER SERIES
INFINITE SHEETED SOLUTIONS (ISS)
ΕΠΙΦΑΝΕΙΕΣ RIEMANN
Algebraic singularities
ΣΕΙΡΕΣ FOURIER
ΕΠΑΝΑΛΗΠΤΙΚΕΣ ΜΕΘΟΔΟΙ ΥΠΟΛΟΓΙΣΜΟΥ
Χάος
Greek
Πανεπιστήμιο Πατρών
University of Patras
Πανεπιστήμιο Πατρών. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών
National Documentation Centre (EKT)
National Archive of PhD Theses
Συλλογή ΕΑΔΔ



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