Title | Interior periodic points of a Lotka–Volterra map
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Par.title | Vnútorné periodické body Lotkovho Volterrovho zobrazenia
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Author info | Peter Maličký
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Author | Maličký Peter 1956- (100%) UMBFP10 - Katedra matematiky
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Source document | Journal of Difference Equations and Applications. Vol. 18, no. 4 (2012), pp. 553-567. - Abingdon : Taylor & Francis Group, 2012
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Keywords |
periodické body
Jacobiho matica - Jacobian matrix
sedlový pevný bod
itinerár
Brouwerova veta
periodic point
saddle fixed point
itinerary
Brouwer theorem
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Language | English
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Country | Great Britian
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systematics | 514
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Annotation | Pre rovinný trojuholník s vrcholmi [0,0], [4,0] a [0,4] skúmame transformáciu F, ktorá zobrazuje bod[x,y] do bodu [xy,x(4-x-y)]. Dokazujeme existenciu vnútorných periodických bodov s periódou n väčšou než 3. Jedna periodická orbita s periódou 6 je vyjadrená explicitne. Dokazujeme tiež, že pre každý dolný sedlový periodický bod existuje vnútorný periodický bod s tým istým itinerárom (vzhľadom na rozklad daný zvislou strednou priečkou). For the plain triangle with vertices [0,0], [4,0] and [0,4] we consider transform F, which maps the point [x,y] to point [xy,x(4-x-y)]. We prove the existence of interior periodic points of periods n greater than 3. One of the periodic orbits of period 6 is given explicitly. We also prove that for any lower periodic saddle point, there is an interior periodic point with the same itinerary (with respect to the natural decomposition of D given by the vertical middle line)
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Public work category | ADC
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No. of Archival Copy | 23322
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Repercussion category | MUKHAMEDOV, Farrukh - ABDUGANIEV, A. On pure quasi-quantum quadratic operators of M-2(C). In Open systems & information dynamics. ISSN 1230-1612, 2013, vol. 20, no. 4, article no. 1350018. BEL'MESOVA, S. S. - EFREMOVA, L. S. On the concept of integrability for discrete dynamical systems. Investigation of wandering points of some trace map. In Springer proceedings in mathematics and statistics : 4th international workshop on nonlinear maps and their applications, NOMA 2013, Zaragoza, 3rd September - 4th September 2013. New York : Springer, 2015. ISBN 978-331912327-1, pp. 127-158. BALIBREA, Francisco. Some problems connected with the thue-morse and Fibonacci sequences. In Advances in dynamical systems and control. ISSN 2198-4182, 2016, vol. 69, pp. 273-293.
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Catal.org. | BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici
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Database | xpca - PUBLIKAČNÁ ČINNOSŤ
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References | PERIODIKÁ-Súborný záznam periodika
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