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Periodic points of the Lotka-Volterra Map and Some Open Problem in Theory of Numbers
Title Periodic points of the Lotka-Volterra Map and Some Open Problem in Theory of Numbers Par.title Periodické body Lotkovho Volterrovho zobrazenia a niektoré otvorené problémy teórie čísel Author info Peter Maličký Author Maličký Peter 1956- (100%) UMBFP10 - Katedra matematiky
Source document AMSE 2010 : 13th International Conference Applications of Mathematics and Statistics in Economy, August 26 - 29, 2010, Demänovská dolina : book of abstracts. S. 25. - Banská Bystrica : Univerzita Mateja Bela, Ekonomická fakulta, 2010 / Kráľ Pavol 1978- ; Laco Peter 1975- ; Zimka Rudolf 1943- ; AMSE 2010 International Conference Applications of Mathematics and Statistics in Economy Keywords periodické body Artinova hypotéza Wieferichovo prvoeíslo prvočíslo Sophie Germainovej periodic point Artin conjecture Wieferich prime Sophie Germain prime Language English Country Slovak Republic systematics 511 Annotation Pre Lotkovo Volterrovo zobrazenie, ktoré zobrazuje na seba trojuholník s vrcholmi (0,0), (4,0) a (0,4) a je definované predpisom F(x,y)=(x(4-x-y),xy), bol dlho otvorený problém vnútorných periodických bodov. Doteraz bol známy iba pevný bod (1,2) a jedna vnútorná periodická orbita s periodou 4. V riešení tohto problému sme urobili podstatný pokrok. Objavili sme hlboký vzťah medzi periodickými bodmi na spodnej strane a vnútornými periodickými bodmi. Zistili sme tiež, že spomínaný problém súvisí s otvorenými problémami teórie čísiel (Artinova hypotéza, Wieferichove prvočísla a prvočísla Sophie Germainovej). For the Lotka-Volterra map, which is defined by F(x,y)=(x(4-x-y),xy) and maps the triangle with vertices (0,0), (4,0) a (0,4) onto itself, the problem of interior periodic ponts was open for a long time. Till now it was known only the fixed point (1,2) and an interior periodic point with period 4. We have made an essential progress in the solution of this problem. We have discovered a deep relation between periodic points on the lower side and interior periodic points. We have also found that the above problem is concerned with some open problems in number theory (the Artin conjecture, Wieferich primes and Sophie Germain primes) Public work category AFH No. of Archival Copy 16588 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ 
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