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Monotone variational recurrence relations : academisch proefschrift ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus prof. dr. L. M. Bouter, in het openbaar te verdedigen ten overstaan van de promotiecommissie van de faculteit der Exacte Wetenschappen op woensdag 21 november 2012 om 15.45 uur in de aula van de universiteit, De Boelelaan 1105
Mramor, Blaž, 1979-
Glavna tema doktorske naloge je Aubry-Matherjeva teorija na mrežah. Bolj natančno, gre za iskanje rešitev monotonih variacijskih rekurzivnih relacij na mrežah. Aubry-Matherjeva teorija zagotavlja ...obstoj tako imenovanih minimalnih Birkhoffovih rešitev, in to za vsak rotacijski vektor. Za iracionalne rotacijske vektorje tvorijo minimalne Brikhoffove rešitve minimalne foliacije ali minimalne laminacije. V prvem delu doktorske naloge konstuiramo tako imenovane navidezne kroge (ghost circles), ki jih dobimo z interpolacijo minimalnih laminacij, in so invariantni glede na gradientni tok podan z variacijskim principom. S pomočjo navideznih krogov pokažemo obstoj rešitev v luknjah v minimalnih lamincijah. Drugi del je namenjen klasifikaciji minimalnih rešitev. V preostalem delu doktorske naloge obravnavamo vprašanje stabilnosti minimalnih foliacij in dokažemo, da so za Liouvillova rotacijska števila minimalne laminacije generične.
Type of material - dissertation
; adult, serious
Publication and manufacture - Amsterdam : [B. Mramor], cop. 2012
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