TY - JOUR AU - Li, Risong AU - Zhao, Yu AU - Wang, Hongqing PY - 2017 TI - Furstenberg families and chaos on uniform limit maps JO - Journal of Nonlinear Sciences and Applications SP - 805--816 VL - 10 IS - 2 AB - Let (\(f_n\)) be a given sequence of continuous selfmaps of a compact metric space \(X\) which converges uniformly to a continuous selfmap \(f\) of a compact metric space \(X\), and let \(F, F_1\), and \(F_2\) be given Furstenberg families. In this paper, we obtain an equivalence condition for the uniform limit map \(f\) to be \(F\)-transitive or weakly \(F\)-sensitive or \(F\)-sensitive or \((F_1, F_2)\)-sensitive and a necessary condition for the uniform limit map \(f\) to be weakly \(F\)-sensitive or \(F\)-sensitive or \((F_1, F_2)\)-sensitive. Our results extend and improve some existing ones. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.02.40 DO - 10.22436/jnsa.010.02.40 ID - Li2017 ER - TY - JOUR TI - Chaotic properties of mappings on a probability space AU - C. Abraham AU - G. Biau AU - B. Cadre JO - J. Math. Anal. Appl. PY - 2002 DA - 2002// VL - 266 ID - Abraham2002 ER - TY - JOUR TI - Uniform convergence and chaotic behavior AU - R. Abu-Saris AU - K. Al-Hami JO - Nonlinear Anal. PY - 2006 DA - 2006// VL - 65 ID - Abu-Saris2006 ER - TY - BOOK TI - Recurrence in topological dynamics. Furstenberg families and Ellis actions AU - E. Akin PB - The University Series in Mathematics, Plenum Press PY - 1997 DA - 1997// CY - New York ID - Akin1997 ER - TY - JOUR TI - On Devaney’s definition of chaos AU - J. Banks AU - J. Brooks AU - G. Cairns AU - G. Davis AU - P. Stacey JO - Amer. Math. Monthly PY - 1992 DA - 1992// VL - 99 ID - Banks1992 ER - TY - JOUR TI - Li-Yorke chaos in a class of nonautonomous discrete systems AU - J. S. Cánovas JO - J. Difference Equ. Appl. PY - 2011 DA - 2011// VL - 17 ID - Cánovas2011 ER - TY - JOUR TI - Chaos in nonautonomous discrete dynamical systems AU - J. Dvořáková JO - Commun. Nonlinear Sci. Numer. Simul. PY - 2012 DA - 2012// VL - 17 ID - Dvořáková2012 ER - TY - JOUR TI - A note on the uniform limit of transitive dynamical systems AU - A. Fedeli AU - A. Le Donne JO - Bull. Belg. Math. Soc. Simon Stevin PY - 2009 DA - 2009// VL - 16 ID - Fedeli2009 ER - TY - JOUR TI - Sensitive dependence on initial conditions AU - E. Glasner AU - B. Weiss JO - Nonlinearity PY - 1993 DA - 1993// VL - 6 ID - Glasner1993 ER - TY - JOUR TI - Weak-mixing implies sensitive dependence AU - L.-F. He AU - X.-H. Yan AU - L.-S. Wang JO - J. Math. Anal. Appl. PY - 2004 DA - 2004// VL - 299 ID - He2004 ER - TY - JOUR TI - A note on shadowing with chain transitivity AU - R.-S. Li JO - Commun. Nonlinear Sci. Numer. Simul. PY - 2012 DA - 2012// VL - 17 ID - Li2012 ER - TY - JOUR TI - A note on stronger forms of sensitivity for dynamical systems AU - R.-S. Li JO - Chaos Solitons Fractals PY - 2012 DA - 2012// VL - 45 ID - Li2012 ER - TY - JOUR TI - A note on uniform convergence and transitivity AU - R.-S. Li JO - Chaos Solitons Fractals PY - 2012 DA - 2012// VL - 45 ID - Li 2012 ER - TY - JOUR TI - The large deviations theorem and ergodic sensitivity AU - R.-S. Li JO - Commun. Nonlinear Sci. Numer. Simul. PY - 2013 DA - 2013// VL - 18 ID - Li 2013 ER - TY - JOUR TI - Erratnm to ''A note on uniform convergence and transitivity [Chaos, Solitons and Fractals 45 (2012), 759–764]'' AU - R.-S. Li AU - H.-Q.Wang JO - Chaos Solitons Fractals PY - 2014 DA - 2014// VL - 59 ID - Li2014 ER - TY - JOUR TI - Sensitivity of set-valued discrete systems AU - H. Liu AU - E.-H. Shi AU - G.-F. Liao JO - Nonlinear Anal. PY - 2009 DA - 2009// VL - 71 ID - Liu2009 ER - TY - JOUR TI - Stronger forms of sensitivity for dynamical systems AU - T. K. S. Moothathu JO - Nonlinearity PY - 2007 DA - 2007// VL - 20 ID - Moothathu2007 ER - TY - JOUR TI - Uniform convergence and transitivity AU - H. Román-Flores JO - Chaos Solitons Fractals PY - 2008 DA - 2008// VL - 38 ID - Román-Flores2008 ER - TY - JOUR TI - Furstenberg families and sensitivity AU - H.-Y. Wang AU - J.-C. Xiong AU - F. Tan JO - Discrete Dyn. Nat. Soc. PY - 2010 DA - 2010 // VL - 2010 ID - Wang2010 ER - TY - JOUR TI - Devaney’s chaos on uniform limit maps AU - K.-S. Yan AU - F.-P. Zeng AU - G.-R. Zhang JO - Chaos Solitons Fractalss PY - 2011 DA - 2011// VL - 44 ID - Yan2011 ER -