On problems of Topological Dynamics in non-autonomous discrete systems

[1]R.L. Adler, A.G. Konheim and M.H. McAndrew, (1965), Topological entropy, Transactions of the American Mathematical Society, 114, No 2, 309-319. 10.2307/1994177AdlerR.L.KonheimA.G.McAndrewM.H.1965Topological entropyTransactions of the American Mathematical Society114230931910.2307/1994177Open DOISearch in Google Scholar

[2]L. Alsedà, J. Llibre and M.Misiurewicz, (2000), Combinatorial Dynamics and Entropy in Dimension One, World Scientific Publishing Co., River Edge.AlsedàL.LlibreJ.MisiurewiczM.2000Combinatorial Dynamics and Entropy in Dimension OneWorld Scientific Publishing Co.River Edge10.1142/4205Search in Google Scholar

[3]J.F. Alves, (2009), What we need to find out the periods of a periodic difference equation, Journal of Difference Equations and Applications, 15, No 8-9, 833-847. 10.1080/10236190802357701AlvesJ.F.2009What we need to find out the periods of a periodic difference equationJournal of Difference Equations and Applications158-983384710.1080/10236190802357701Open DOISearch in Google Scholar

[4]Z. AlSharawi, J. Angelos, S. Elaydi and L. Rakesh, (2006), An extension of Sharkovsky’s theorem to periodic difference equations, Journal of Mathematical Analysis and Applications, 316, No 1, 128-141. 10.1016/j.jmaa.2005.04.059AlSharawiZ.AngelosJ.ElaydiS.RakeshL.2006An extension of Sharkovsky’s theorem to periodic difference equationsJournal of Mathematical Analysis and Applications316112814110.1016/j.jmaa.2005.04.059Open DOISearch in Google Scholar

[5]R. Azizi, Nonautonomous Riccati difference equation with real k–periodic (k ≥ 1) coefficients, submitted to Journal of Difference Equations and Applications.AziziR.Nonautonomous Riccati difference equation with real k–periodic (k ≥ 1) coefficientssubmitted to Journal of Difference Equations and Applications.Search in Google Scholar

[6]F. Balibrea, (2016), Los secretos de algunas sucesiones de números enteros, MATerials MATemàtics. Publicaciò electrònica de divulgació del Departament de Matemàtiques de la Universitat Autònoma de Barcelona, treball no. 2, 32 pp.BalibreaF.2016Los secretos de algunas sucesiones de números enterosMATerials MATemàtics. Publicaciò electrònica de divulgació del Departament de Matemàtiques de la Universitat Autònoma de Barcelona, treball no. 232Search in Google Scholar

[7]F. Balibrea and A. Cascales, (2015), On forbidden sets, Journal of Difference Equations and Applications, 21, No 10, 974-996. 10.1080/10236198.2015.1061517BalibreaF.CascalesA.2015On forbidden setsJournal of Difference Equations and Applications211097499610.1080/10236198.2015.1061517Open DOISearch in Google Scholar

[8]F.Balibrea and R.Chacón, (2011), A simple non-autonomous system with complicated dynamics, Journal of Difference Equations and Applications, 17, No 2, 131-136. 10.1080/10236198.2010.549016BalibreaF.ChacónR.2011A simple non-autonomous system with complicated dynamicsJournal of Difference Equations and Applications17213113610.1080/10236198.2010.549016Open DOISearch in Google Scholar

[9]F. Balibrea and A. Linero, (2003), On the periodic structure of delayed difference equations of the form x_n = f(x_n - k) on 𝕀 and 𝕊¹, Journal of Difference Equations and Applications, 9, No 3-4, 359-371. 10.1080/1023619021000047789BalibreaF.LineroA.2003On the periodic structure of delayed difference equations of the form x_n = f(x_n - k) on 𝕀 and 𝕊¹Journal of Difference Equations and Applications93-435937110.1080/1023619021000047789Open DOISearch in Google Scholar

[10]F. Balibrea, T. Caraballo, P. E. Kloeden and J. Valero, (2010), Recent developments in Dynamical Systems: three perspectives, International Journal of Bifurcation and Chaos, 20, No 9, 2591-2636. 10.1142/S0218127410027246BalibreaF.CaraballoT.KloedenP. E.ValeroJ.2010Recent developments in Dynamical Systems: three perspectivesInternational Journal of Bifurcation and Chaos2092591263610.1142/S0218127410027246Open DOISearch in Google Scholar

[11]F. Balibrea and M. Victoria Caballero, (2013), Stability of orbits via Lyapunov exponents in autonomous and nonautonomous systems, International Journal of Bifurcation and Chaos, 23, No 7, 1350127 [11 pages]. 10.1142/S0218127413501277BalibreaF.Victoria CaballeroM.2013Stability of orbits via Lyapunov exponents in autonomous and nonautonomous systemsInternational Journal of Bifurcation and Chaos237135012711 pages10.1142/S0218127413501277Open DOISearch in Google Scholar

[12]F. Balibrea, F. Esquembre and A.Linero, (1995), Smooth triangular maps of type 2^∞ with positive topological entropy, International Journal of Bifurcation and Chaos, 5, No 5, 1319-1324. 10.1142/S0218127495000983BalibreaF.EsquembreF.LineroA.1995Smooth triangular maps of type 2^∞ with positive topological entropyInternational Journal of Bifurcation and Chaos551319132410.1142/S0218127495000983Open DOISearch in Google Scholar

[13]F. Balibrea, J. L. G. Guirao and J.I. Muñoz Casado, (2001), Description of ω–limit sets of a triangular map on I², Far East Journal of Dynamical Systems, 3, 87-101.BalibreaF.GuiraoJ. L. G.Muñoz CasadoJ.I.2001Description of ω–limit sets of a triangular map on I²Far East Journal of Dynamical Systems387101Search in Google Scholar

[14]F. Balibrea, J. Smítal and M.Stefánková, (2005), The three versions of distributional chaos, Chaos, Solitons and Fractals, 23, No 5, 1581-1583. 10.1016/j.chaos.2004.06.011BalibreaF.SmítalJ.StefánkováM.2005The three versions of distributional chaosChaos, Solitons and Fractals2351581158310.1016/j.chaos.2004.06.011Open DOISearch in Google Scholar

[15]F. Balibrea and P. Oprocha, (2012), Weak mixing and chaos in nonautonomous discrete systems, Applied Mathematics Letters, 25, No 8, 1135-1141. 10.1016/j.aml.2012.02.021BalibreaF.OprochaP.2012Weak mixing and chaos in nonautonomous discrete systemsApplied Mathematics Letters2581135114110.1016/j.aml.2012.02.021Open DOISearch in Google Scholar

[16]F. Balibrea-Iniesta, C. Lopesino, S. Wiggins and A. Mancho, (2015), Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon Map, International Journal of Bifurcation and Chaos, Vol 25, No 12, 1550172 [14 pages]. 10.1142/S0218127415501722Balibrea-IniestaF.LopesinoC.WigginsS.ManchoA.2015Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon MapInternational Journal of Bifurcation and Chaos2512155017214 pages10.1142/S0218127415501722Open DOISearch in Google Scholar

[17]F. Benford, (1938), The Law of Anomalous Numbers, Proceedings of the American Philosophical Society, 78, No 4, 551-572.BenfordF.1938The Law of Anomalous NumbersProceedings of the American Philosophical Society784551572Search in Google Scholar

[18]F. Blanchard, E. Glasner, S. Kolyada and A. Maass, (2002), On Li-Yorke pairs, Journal für die reine und angewandte Mathematik (Crelles Journal), 547, 51-68. 10.1515/crll.2002.053BlanchardF.GlasnerE.KolyadaS.MaassA.2002On Li-Yorke pairsJournal für die reine und angewandte Mathematik (Crelles Journal)547516810.1515/crll.2002.053Open DOISearch in Google Scholar

[19]A. Berger, (2005), Multi-dimensional dynamical systems and Benford’s Law, Discrete and Continuous Dynamical Systems - Series A, 13, 1, 219-237. 10.3934/dcds.2005.13.219BergerA.2005Multi-dimensional dynamical systems and Benford’s LawDiscrete and Continuous Dynamical Systems - Series A13121923710.3934/dcds.2005.13.219Open DOISearch in Google Scholar

[20]A. Berger and S. Siegmund, (2007), On the distribution of mantissae in nonautonomous difference equations, Journal of Difference Equations and Applications, 13, No 8-9, 829-845. 10.1080/10236190701388039BergerA.SiegmundS.2007On the distribution of mantissae in nonautonomous difference equationsJournal of Difference Equations and Applications138-982984510.1080/10236190701388039Open DOISearch in Google Scholar

[21]A. Berger, (2011), Some dynamical properties of Benford sequences, Journal of Difference Equations and Applications, 17, No 2, 137-159. 10.1080/10236198.2010.549012BergerA.2011Some dynamical properties of Benford sequencesJournal of Difference Equations and Applications17213715910.1080/10236198.2010.549012Open DOISearch in Google Scholar

[22]Bogenschütz, (1992), Entropy, pressure, and a variational principle for random dynamical systems, Random Comp., 1, 219-227.Bogenschütz1992Entropy, pressure, and a variational principle for random dynamical systemsRandom Comp.1219227Search in Google Scholar

[23]R. Bowen, (1971), Entropy for group endomorphisms and homogeneous spaces, Transactions of the American Mathematical Society, 153, 401-414. 10.1090/S0002-9947-1971-0274707-XBowenR.1971Entropy for group endomorphisms and homogeneous spacesTransactions of the American Mathematical Society15340141410.1090/S0002-9947-1971-0274707-XOpen DOISearch in Google Scholar

[24]E. Camouzis and G. Ladas, (2007), Periodically forced Pielou’s equation, Journal of Mathematical Analysis and Applications, 333, No 1, 117-127. 10.1016/j.jmaa.2006.10.096CamouzisE.LadasG.2007Periodically forced Pielou’s equationJournal of Mathematical Analysis and Applications333111712710.1016/j.jmaa.2006.10.096Open DOISearch in Google Scholar

[25]E. Camouzis and R. DeVault, (2003), The Forbidden Set of xn+1=p+xn−1xn,$\begin{array}{} x_{n+1} = p + \frac{x_{n-1}}{x_{n}}, \end{array} $ Journal of Difference Equations and Applications, 9, No. 8, 739-750. 10.1080/1023619021000042144CamouzisE.DeVaultR.2003The Forbidden Set of xn+1=p+xn−1xn,$\begin{array}{} x_{n+1} = p + \frac{x_{n-1}}{x_{n}}, \end{array} $Journal of Difference Equations and Applications9873975010.1080/1023619021000042144Open DOISearch in Google Scholar

[26]E. Camouzis and G. Ladas, (2007), Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall/CRC.CamouzisE.LadasG.2007Dynamics of Third-Order Rational Difference Equations with Open Problems and ConjecturesChapman and Hall/CRC10.1201/9781584887669Search in Google Scholar

[27]J. S. Cánovas and A. Linero, (2006), Periodic structure of alternating continuous interval maps, Journal of Difference Equations and Applications, 12, No 8, 847-858. 10.1080/10236190600772515CánovasJ. S.LineroA.2006Periodic structure of alternating continuous interval mapsJournal of Difference Equations and Applications12884785810.1080/10236190600772515Open DOISearch in Google Scholar

[28]J. S. Cánovas, (2006), On ω–limit sets of non-autonomous discrete systems, Journal of Difference Equations and Applications, 12, No 1, 95-100. 10.1080/10236190500424274CánovasJ. S.2006On ω–limit sets of non-autonomous discrete systemsJournal of Difference Equations and Applications1219510010.1080/10236190500424274Open DOISearch in Google Scholar

[29]J. S. Cánovas, (2013), Recent results on non-autonomous discrete systems, Boletín de la Sociedad Española de Matemática Aplicada, 51, No 1, 33-40. 10.1007/BF03322551CánovasJ. S.2013Recent results on non-autonomous discrete systemsBoletín de la Sociedad Española de Matemática Aplicada511334010.1007/BF03322551Open DOISearch in Google Scholar

[30]J.M. Cushing and S.M. Henson, (2002), A Periodically Forced Beverton-Holt Equation, Journal of Difference Equations and Applications, 8, No 12, 1119-1120. 10.1080/1023619021000053980CushingJ.M.HensonS.M.2002A Periodically Forced Beverton-Holt EquationJournal of Difference Equations and Applications8121119112010.1080/1023619021000053980Open DOISearch in Google Scholar

[31]B. Demir and S. Koçak, (2001), A note on positive Lyapunov exponent and sensitive dependence on initial conditions, Chaos, Solitons and Fractals, 12, No 11, 2119-2121. 10.1016/S0960-0779(00)00160-0DemirB.KoçakS.2001A note on positive Lyapunov exponent and sensitive dependence on initial conditionsChaos, Solitons and Fractals12112119212110.1016/S0960-0779(00)00160-0Open DOISearch in Google Scholar

[32]M. De la Sen, (2008), The generalized Beverton-Holt equation and the control of populations, Applied Mathematical Modelling, 32, No 11, 2312-2328. 10.1016/j.apm.2007.09.007De la SenM.2008The generalized Beverton-Holt equation and the control of populationsApplied Mathematical Modelling32112312232810.1016/j.apm.2007.09.007Open DOISearch in Google Scholar

[33]S. Elaydi, (2005), An Introduction to Difference Equations, Springer-Verlag, Berlin.ElaydiS.2005An Introduction to Difference EquationsSpringer-VerlagBerlinSearch in Google Scholar

[34]H. Furstenberg, (1981), Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, New Jersey.FurstenbergH.1981Recurrence in Ergodic Theory and Combinatorial Number TheoryPrinceton University PressNew Jersey10.1515/9781400855162Search in Google Scholar

[35]M. Grinc and L’. Snoha (2000), Jungck theorem for triangular maps and related results, Applied General Topology, 1, No 1, 83-92. 10.4995/agt.2000.3025GrincM.SnohaĽ.2000Jungck theorem for triangular maps and related resultsApplied General Topology11839210.4995/agt.2000.3025Open DOISearch in Google Scholar

[36]E. A. Grove and G. Ladas, (2004), Periodicities in Nonlinear Difference Equations, Chapman and Hall/CRC.GroveE. A.LadasG.2004Periodicities in Nonlinear Difference EquationsChapman and Hall/CRC10.1201/9781420037722Search in Google Scholar

[37]K. Janková and J. Smítal, (1995), Maps with random perturbations are generically not chaotic, International Journal of Bifurcation and Chaos, 5, No 5, 1375-1378. 10.1142/S0218127495001058JankováK.SmítalJ.1995Maps with random perturbations are generically not chaoticInternational Journal of Bifurcation and Chaos551375137810.1142/S0218127495001058Open DOISearch in Google Scholar

[38]N. Joshi, D. Burtonclay and R.G.Halburd, (1992), Nonlinear nonautonomous discrete dynamical systems from a general discrete isomonodromy problem, Letters in Mathematical Physics, 26, No 2, 123-131.10.1007/BF00398809JoshiN.BurtonclayD.HalburdR.G.1992Nonlinear nonautonomous discrete dynamical systems from a general discrete isomonodromy problemLetters in Mathematical Physics262123131Open DOISearch in Google Scholar

[39]R. Kempf, (2002), On Ω–limit Sets of Discrete-time Dynamical Systems, Journal of Difference Equations and Applications, 8, No 12, 1121-1131. 10.1080/10236190290029024KempfR.2002On Ω–limit Sets of Discrete-time Dynamical SystemsJournal of Difference Equations and Applications8121121113110.1080/10236190290029024Open DOISearch in Google Scholar

[40]S. Kolyada and L. Snoha, (1992), On ω-limit sets of triangular maps, Real Analysis Exchange 18, 115-130.KolyadaS.SnohaL.1992On ω-limit sets of triangular mapsReal Analysis Exchange1811513010.2307/44133050Search in Google Scholar

[41]S. Kolyada and Ľ. Snoha, (1996), Topological entropy of nonautonomous dynamical systems, Random & Computational Dynamics, 4, 205-233.KolyadaS.SnohaĽ.1996Topological entropy of nonautonomous dynamical systemsRandom & Computational Dynamics4205233Search in Google Scholar

[42]S. Kolyada, Ľ. Snoha and S.Trofimchuk, (2004), On Minimality of Nonautonomous Dynamical Systems, Nonlinear Oscillations, 7, No 1, 83-89. 10.1023/B:NONO.0000041798.79176.94KolyadaS.SnohaĽ.TrofimchukS.2004On Minimality of Nonautonomous Dynamical SystemsNonlinear Oscillations71838910.1023/B:NONO.0000041798.79176.94Open DOISearch in Google Scholar

[43]S. Kolyada, Ľ. Snoha and S.Trofimchuk, (2001), Noninvertible minimal maps, Fundamenta Mathematicae, 168, No 2, 141-163.10.4064/fm168-2-5KolyadaS.SnohaĽ.TrofimchukS.2001Noninvertible minimal mapsFundamenta Mathematicae1682141163Open DOISearch in Google Scholar

[44]S. Kolyada, M. Misiurewicz and Ľ. Snoha, (1999), Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval, Fundamenta Mathematicae, 160, No 2, 161-181.KolyadaS.MisiurewiczM.SnohaĽ.1999Topological entropy of nonautonomous piecewise monotone dynamical systems on the intervalFundamenta Mathematicae160216118110.4064/fm-160-2-161-181Search in Google Scholar

[45]M.R.S. Kulenović and G. Ladas, (2001), Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures, Chapman and Hall/CRC.KulenovićM.R.S.LadasG.2001Dynamics of Second Order Rational Difference Equations: With Open Problems and ConjecturesChapman and Hall/CRC10.1201/9781420035384Search in Google Scholar

[46]C. Lopesino, F. Balibrea-Iniesta, S. Wiggins and A.M. Mancho, (2015), The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions, International Journal of Bifurcation and Chaos, 25, No 13, 1550184 [18 pages]. 10.1142/S0218127415501849LopesinoC.Balibrea-IniestaF.WigginsS.ManchoA.M.2015The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous VersionsInternational Journal of Bifurcation and Chaos2513155018418 pages10.1142/S0218127415501849Open DOISearch in Google Scholar

[47]J. Moser, (1973), Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics (AM-77), Princeton University Press, Princeton.MoserJ.1973Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics (AM-77)Princeton University PressPrincetonSearch in Google Scholar

[48]J. Rubió-Massegú and V. Mañosa, (2007), Normal forms for rational difference equations with applications to the global periodicity problem, Journal of Mathematical Analysis and Applications, 332, No 2, 896-918. 10.1016/j.jmaa.2006.10.061Rubió-MassegúJ.MañosaV.2007Normal forms for rational difference equations with applications to the global periodicity problemJournal of Mathematical Analysis and Applications332289691810.1016/j.jmaa.2006.10.061Open DOISearch in Google Scholar

[49]H. Sedaghat, (2003), Nonlinear Difference Equations. Theory and Applications to Social Science Models, Springer-Verlag, Berlin.SedaghatH.2003Nonlinear Difference EquationsTheory and Applications to Social Science ModelsSpringer-VerlagBerlin10.1007/978-94-017-0417-5Search in Google Scholar

[50]Y. Shi, L. Zhang, P. Yu and Q. Huang, (2015),Chaos in Periodic Discrete Systems, International Journal of Bifurcation and Chaos, 25, No 1, 1550010 [21 pages]. 10.1142/S0218127415500108ShiY.ZhangL.YuP.HuangQ.2015Chaos in Periodic Discrete SystemsInternational Journal of Bifurcation and Chaos251155001021 pages10.1142/S0218127415500108Open DOISearch in Google Scholar

[51]S. Stević, (2013), Domains of undefinable solutions of some equations and systems of difference equations, Applied Mathematics and Computation, 219, No 24, 11206-11213. 10.1016/j.amc.2013.05.017StevićS.2013Domains of undefinable solutions of some equations and systems of difference equationsApplied Mathematics and Computation21924112061121310.1016/j.amc.2013.05.017Open DOISearch in Google Scholar

[52]L. Szała, (2015), Chaotic behaviour of uniformly convergent non-autonomous systems with randomly perturbed trajectories, Journal of Difference Equations and Applications, 21, No 7, 592-605. 10.1080/10236198.2015.1044448SzałaL.2015Chaotic behaviour of uniformly convergent non-autonomous systems with randomly perturbed trajectoriesJournal of Difference Equations and Applications21759260510.1080/10236198.2015.1044448Open DOISearch in Google Scholar

[53]J. Wright, (2913), Periodic systems of population models and enveloping functions, Computers & Mathematics with Applications, 66, No 11, 2178-2195. 10.1016/j.camwa.2013.08.013WrightJ.2913Periodic systems of population models and enveloping functionsComputers & Mathematics with Applications66112178219510.1016/j.camwa.2013.08.013Open DOISearch in Google Scholar

[54]S. Wiggins, (2003), Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer.WigginsS.2003Introduction to Applied Nonlinear Dynamical Systems and ChaosSpringerSearch in Google Scholar

[55]W.-B. Zhang, (2006), Discrete Dynamical Systems, Bifurcations and Chaos in Economics, Elsevier Science, Amsterdam.ZhangW.-B.2006Discrete Dynamical Systems, Bifurcations and Chaos in EconomicsElsevier ScienceAmsterdamSearch in Google Scholar