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Title Minimality for actions of abelian semigroups on compact spaces with a free interval Author info Matúš Dirbák, Roman Hric ... [et al.] Author Dirbák Matúš 1983- (20%) UMBFP10 - Katedra matematiky
Co-authors Hric Roman 1970- (20%) UMBFP10 - Katedra matematiky
Maličký Peter 1956- (20%) UMBFP10 - Katedra matematiky
Snoha Ľubomír 1955- (20%) UMBFP10 - Katedra matematiky
Špitalský Vladimír 1973- (20%) UMBFP10 - Katedra matematiky
Source document Ergodic Theory and Dynamical Systems. Vol. 39, no. 11 (2019), pp. 2968-2982. - Cambridge : Cambridge University Press, 2019 Keywords Abelovské grupy - Abelian groups minimal group action minimal sets matematika - mathematics Form. Descr. články - journal articles Language English Country Great Britian URL Link na plný text Public work category ADC No. of Archival Copy 46104 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
unrecognised
Title Periodic points of Lotka-Volterra map and their relation to number theory Author info Peter Maličký Author Maličký Peter 1956- (100%)
Source document Czech-Slovak workshop on discrete dynamical systems 2018. Pp. 18. - Banská Bystrica : Fakulta prírodných vied Univerzity Mateja Bela, 2018 ; Czech-Slovak workshop on dynamical systems 2018 workshop Keywords matematika - mathematics periodické body Form. Descr. abstrakty - abstracts Language English Country Slovak Republic URL Link na zdrojový dokument Public work category GHG No. of Archival Copy 4090 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ 
article
Title Periodic points of Lotka-Volterra map and their relation to number theory Author info Peter Maličký Author Maličký Peter 1956- (100%)
Source document Czech-Slovak workshop on discrete dynamical systems 2016. Pp. 10-11. - Opava : Slezská univerzita v Opavě, 2016 ; Czech-Slovak workshop on discrete dynamical systems 2016 workshop Keywords matematika - mathematics periodické body Form. Descr. abstrakty - abstracts Language English Country Czech Republic URL Link na zdrojový dokument Public work category GHG No. of Archival Copy 3496 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title A special modification of the Lotka-Volterra map and its interior periodic points Author info Peter Maličký Author Maličký Peter 1956- (100%)
Source document Czech-Slovak workshop on discrete dynamical systems 2014. Pp. 10-11. - Opava : Slezská univerzita v Opavě, 2014 ; Czech-Slovak workshop on discrete dynamical systems 2014 workshop Keywords matematika - mathematics periodické body Form. Descr. abstrakty - abstracts Language English Country Slovak Republic URL Link na zdrojový dokument Public work category GHG No. of Archival Copy 3434 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title Interior periodic points of a Lotka–Volterra map Par.title Vnútorné periodické body Lotkovho Volterrovho zobrazenia Author info Peter Maličký Author Maličký Peter 1956- (100%) UMBFP10 - Katedra matematiky
Source document Journal of Difference Equations and Applications. Vol. 18, no. 4 (2012), pp. 553-567. - Abingdon : Taylor & Francis Group, 2012 Keywords periodické body Jacobiho matica - Jacobian matrix sedlový pevný bod itinerár Brouwerova veta periodic point saddle fixed point itinerary Brouwer theorem Language English Country Great Britian systematics 514 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) Public work category ADC No. of Archival Copy 23322 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.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika unrecognised
Title On the existence of tori in Asada's two-regional model Author info Peter Maličký, Rudolf Zimka Author Maličký Peter 1956- (50%) UMBFP10 - Katedra matematiky
Co-authors Zimka Rudolf 1943- (50%) UMBEF05 - Katedra kvantitatívnych metód a informačných systémov
Source document Nonlinear Analysis : Real World Applications. Vol. 13, no. 2 (2012), pp. 710-724. - Oxford : Elsevier Ltd., 2012 Keywords dynamical model equilibrium matrix of linear approximation eigenvalues normal form of differential equations on invariant surface bifurcation equations torus Language English Country Great Britian systematics 51 URL Link do databázy WoS Public work category ADC No. of Archival Copy 22387 Repercussion category INABA, Toshio - ASADA, Toichiro. On dynamics of a three-country kaldorian model of business cycles with fixed exchange rates. In Games and dynamics in economics : essays in honor of Akio Matsumoto. Singapore : Springer Singapore, 2020. ISBN 978-981153623-6, pp. 103-124.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika unrecognised
Title Backward orbits of transitive maps Par.title Spätné orbity tranzitívnych zobrazení Author info Peter Maličký Author Maličký Peter 1956- (100%) UMBFP10 - Katedra matematiky
Source document Journal of Difference Equations and Applications. Vol. 18, no. 7 (2012), pp. 1193-1203. - Abingdon : Taylor & Francis Group, 2012 Keywords spätná orbita tranzitívne zobrazenia reziduálna množina analytická množina Bairova vlastnosť backward orbits transitive maps residual set analytic set property of Baire Language English Country Great Britian systematics 517 Annotation Pre diskrétny dynamický priestor určený poským priestorom X a spojitým zobrazením f priestoru X do seba skúmame množinu D tých bodov, ktoré majú nejakú hustú spätnú orbitu. Dokazujeme, že pre tranzitívne zobrazenie f je množina D analytická, ktorá má mohutnusť kontinua dokonca lokálne. Za predpokladu, ze f je navyše skoro slabo otvorené je množina D reziduálna. For a discrete dynamical system given by a Polish space X and a continuous selfmap f of X we investigate the set D of all points which have some dense backward orbit. It is proved that if f is a topologically transitive map then D is an analytic set which has the continuum power even locally. Under the additional assumption that f is nearly feebly open, the set D is residual Public work category ADC No. of Archival Copy 23321 Repercussion category MOOTHATHU, T. K. Subrahmonian. The speed with which an orbit approaches a limit point. In Journal of difference equations and applications. ISSN 1023-6198, 2012, vol. 18, no. 10, pp. 1611-1621.
DIRBAK, Matus - SNOHA, Lubomir - SPITALSKY, Vladimir. Minimality, transitivity, mixing and topological entropy on spaces with a free interval. In Ergodic theory and dynamical systems. ISSN 0143-3857, 2013, vol. 33, pp. 1786-1812.
BLANCHARD, François - HUANG, Wen - SNOHA, Ľubomír. Topological size of scrambled sets. In Colloquium mathematicum. ISSN 0010-1354, 2008, vol. 110, no. 2, pp. 293-361.
KOLYADA, S. - SNOHA, L. - TROFIMCHUK, S. Noninvertible minimal maps. In Fundamenta mathematicae. ISSN 0016-2736, 2001, vol. 168, no. 2, pp. 141-163.
KOLYADA, Sergii - SNOHA, Lubomir - TROFIMCHUK, Sergei. Minimal sets of fibre-preserving maps in graph bundles. In Mathemathische Zeitschrift. ISSN 0025-5874, 2014, vol. 278, no. 1-2, pp. 575-614.
TAKACS, Michal. Generic chaos on graphs. In Journal of difference equations and applications. ISSN 1023-6198, 2016, vol. 22, no. 1, pp. 1-21.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika unrecognised
Title On the equilibrium stability in a two-regional model under flexible exchange rates Par.title Stabilność równowagi w dwuregionalnym modelu przy założeniu elastycznych kursów wymiany Author info Peter Maličký, Rudolf Zimka Author Maličký Peter 1956- (50%) UMBFP13 - Dekanát Fakulty prírodných vied
Co-authors Zimka Rudolf 1943- (50%) UMBEF05 - Katedra kvantitatívnych metód a informačných systémov
Source document Statystyka i ryzyko. S. 196-211. - Wrocław : University of Economics, 2012 / Rusnak Zofia ; Mielecka-Kubień Zofia Keywords dynamical model equilibrium asymptotical stability Language English Country Poland systematics 007 Public work category AEC No. of Archival Copy 23045 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ unrecognised
Title On number of interior periodic points of a Lotka-Voltera map Author info Peter Maličký Author Maličký Peter 1956- (100%) UMBFP10 - Katedra matematiky
Source document Acta Universitatis Matthiae Belii : series Mathematics : special issue dedicated to the 75th birthday of Professor Beloslav Riečan, No. 19 (2011). S. 21-30. - Banská Bystrica : Ústav vedy a výskumu Univerzity Mateja Bela v Banskej Bystrici, 2011 / Haviar Miroslav 1965- Note Bibl.: s. 30 Keywords periodic point Jacobiho matica - Jacobian matrix saddle fixed point itinerary Brouwer theorem Language English Country Slovak Republic systematics 51 Annotation Res. angl. Public work category AED No. of Archival Copy 20700 Repercussion category 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.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ article
Title On the construction of non-invertible minimal skew products Par.title O konštrukcii neinvertovateľných minimálnych šikmých súčinov Author info Matúš Dirbák, Peter Maličký Author Dirbák Matúš 1983- (50%) UMBFP10 - Katedra matematiky
Co-authors Maličký Peter 1956- (50%) UMBFP10 - Katedra matematiky
Source document Journal of Mathematical Analysis and Applications. Vol. 375, no. 2 (2011), pp. 436-442. - San Diego : Academic Press, 2011 Keywords topologická entropia - topological entropy rozšírenie - extension šikmý súčin trojuholníkové zobrazenia minimálna akcia grupy homogénny priestor súvislej kompaktnej grupy skew product triangular maps minimal group action homogeneous space of a compact connected group Language English Country United States of America systematics 515.1 Annotation Nech X,Z sú nekonečné kompaktné metrické priestory. Ukazujeme, že ak grupa H(Z) homeomorfizmov priestoru Z obsahuje oblúkovo súvislú podgrupu G(Z), ktorej akcia na Z je minimálna, potom každé minimálne zobrazenie f na X (invertovateľné alebo aj neinvertovateľné) pripúšťa minimálne rozšírenie ako šikmý súčin F=(f,g_x) na XxZ s vláknovými zobrazeniami g_x v uzávere podgrupy G(Z). V invertovateľnom prípade tento výsledok bol dokázaný Glasnerom a Weissom roku 1979. Tiež prispievame k opisu triedy C priestorov Z pripušťajúcich grupu G(Z) so spomenutou vlastnosťou. Konkrétne ukazujeme, že táto trieda je uzavretá vzhľadom na spočítateľné súčiny a obsahuje nekonečné spočítateľné súčiny variet, z ktorých nekonečne veľa má neprázdnu hranicu. Ďalej ukazujeme, že podtrieda triedy C tvorená kompaktnými metrickými priestormi Z, ktoré pripúšťajú oblúkovo súvislú grupu izometrií I(Z) s minimálnou akciou na Z sa zhoduje s triedou homogénnych priestorov súvislých kompaktných metrizovateľných grúp. Let X,Z be infinite compact metric spaces. We show that if the group H(Z) of the homeomorphisms of Z has an arc-wise connected subgroup G(Z) whose action on Z is minimal then every minimal map f on X (invertible or not) admits a minimal skew product extension F=(f,g_x) on XxZ with the fibre maps g_x in the closure of G(Z). In the invertible case this was proved by Glasner and Weiss in 1979. We also contribute to the description of the class C of those spaces Z which admit a group G(Z) with the mentioned property. Namely, we show that this class is closed with respect to countable products and contains all countably infinite products of compact connected manifolds, infinitely many of which have nonempty boundary. Further, we show that the subclass of C formed by all compact metric spaces Z which admit an arc-wise connected group I(Z) of isometries with a minimal action on Z coincides with the class of all homogeneous spaces of compact connected metrizable groups Public work category ADC No. of Archival Copy 20204 Repercussion category KOLJADA, Sergij. Topologična dinamika minimalinisti, entropija ta chaos. Kiev : Nacionalina akademija nauk Ukrajini, Institut matematiki, 2011. ISBN 978-966-02-6280-5.
KOLYADA, Sergii - SNOHA, Lubomir - TROFIMCHUK, Sergei. Minimal sets of fibre-preserving maps in graph bundles. In Mathematische Zeitschrift. ISSN 0025-5874, 2014, vol. 278, no. 1-2, pp. 575-614.
DeVRIES, J. Topological dynamical systems : an introduction to the dynamics of continuous mappings. Berlin : DeGruyter, 2014. DeGruyter Studies in Mathematics, vol. 49. 498 p. ISBN 978-3-11-034240-6.
SOTOLA, Jakub - TROFIMCHUK, Sergei. Construction of minimal non-invertible skew-product maps on 2-manifolds. In Proceedings of the American mathematical society. ISSN 0002-9939, 2016, vol. 144, no. 2, pp. 723-732.
Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika unrecognised