%0 Journal Article %T Multi-sensitivity, syndetical sensitivity and the asymptotic average- shadowing property for continuous semi-flows %A Li, Risong %A Lu, Tianxiu %A Zhao, Yu %A Wang, Hongqing %A Liang, Haihua %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 9 %@ ISSN 2008-1901 %F Li2017 %X In this paper, for a continuous semi-flow \(\theta\) on a compact metric space \(E\) with the asymptotic average-shadowing property (AASP), we show that if the almost periodic points of \(\theta\) are dense in \(E\) then \(\theta\) is multi-sensitive and syndetically sensitive. Also, we show that if \(\theta\) is a Lyapunov stable semi-flow with the AASP, then the space \(E\) is trivial. Consequently, a Lyapunov stable semi-flow with the AASP is minimal. Furthermore, we prove that for a syndetically transitive continuous semi-flow on a compact metric space, sensitivity is equivalent to syndetical sensitivity. As an application, we show that for a continuous semi-flow \(\theta\) on a compact metric space \(E\) with the AASP, if the almost periodic points of \(\varphi\) are dense in \(E\) then \(\theta\) is syndetically sensitive. {Moreover, we prove that for any continuous semi-flow \(\theta\) on a compact metric space, it has the AASP if and only if so does its inverse limit \((\widetilde{E}, \widetilde{\theta})\), and if only if so does its lifting continuous semi-flow \((\widehat{E}, \widehat{\theta})\). Also, an example which contains two numerical experiments is given. Our results extend some corresponding and existing ones. %9 journal article %R 10.22436/jnsa.010.09.34 %U http://dx.doi.org/10.22436/jnsa.010.09.34 %P 4940--4953 %0 Journal Article %T A variational principle for impulsive semiflows %A J. F. Alves %A M. Carvalho %A C. H. Vásquez %J J. Differential Equations %D 2015 %V 259 %F Alves2015 %0 Book %T Topological theory of dynamical systems %A N. Aoki %A K. Hiraide %D 1994 %I Recent advances, North-Holland Mathematical Library, North-Holland Publishing Co. %C Amsterdam %F Aoki1994 %0 Journal Article %T Flows with the (asymptotic) average shadowing property on three-dimensional closed manifolds %A A. Arbieto %A R. Ribeiro %J Dyn. Syst. %D 2011 %V 26 %F Arbieto2011 %0 Journal Article %T Periodic prime knots and topologically transitive flows on 3-manifolds %A W. Basener %A M. C. Sullivan %J Topology Appl. %D 2006 %V 153 %F Basener2006 %0 Journal Article %T Dynamical properties of a perceptron learning process: structural stability under numerics and shadowing %A A. Bielecki %A J. Ombach %J J. Nonlinear Sci. %D 2011 %V 21 %F Bielecki2011 %0 Journal Article %T Small perturbations of chaotic dynamical systems %A M. Blank %J (Russian); translated from Uspekhi Mat. Nauk, 44 (1989), 3–28, Russian Math. Surveys %D 1989 %V 44 %F Blank1989 %0 Book %T Equilibrium states and the ergodic theory of Anosov diffeomorphisms %A R. Bowen %D 1975 %I Lecture Notes in Mathematics, Springer-Verlag %C Berlin-New York %F Bowen1975 %0 Journal Article %T Expansive one-parameter flows %A R. Bowen %A P. Walters %J J. Differential Equations %D 1972 %V 12 %F Bowen1972 %0 Journal Article %T Specification on the interval %A J. Buzzi %J Trans. Amer. Math. Soc. %D 1997 %V 349 %F Buzzi 1997 %0 Journal Article %T Recurrence and the shadowing property %A C.-K. Chu %A K.-S. Koo %J Topology Appl. %D 1996 %V 71 %F Chu1996 %0 Book %T Isolated invariant sets and the Morse index %A C. Conley %D 1978 %I CBMS Regional Conference Series in Mathematics, American Mathematical Society %C Providence, R.I. %F Conley 1978 %0 Book %T Ergodic theory on compact spaces %A M. Denker %A C. Grillenberger %A K. Sigmund %D 1976 %I Lecture Notes in Mathematics, Springer- Verlag %C Berlin-New York %F Denker1976 %0 Journal Article %T Shadowing property of continuous maps %A T. Gedeon %A M. Kuchta %J Proc. Amer. Math. Soc. %D 1992 %V 115 %F Gedeon1992 %0 Journal Article %T The asymptotic average-shadowing property and transitivity for flows %A R.-B. Gu %J Chaos Solitons Fractals %D 2009 %V 41 %F Gu2009 %0 Journal Article %T The average-shadowing property and topological ergodicity for flows %A R.-B. Gu %A W.-J. Guo %J Chaos Solitons Fractals %D 2005 %V 25 %F Gu2005 %0 Journal Article %T The average-shadowing property and transitivity for continuous flows %A R.-B. Gu %A Y.-Q. Sheng %A Z.-J. Xia %J Chaos Solitons Fractals %D 2005 %V 23 %F Gu2005 %0 Journal Article %T Some dynamical properties of continuous semi-flows having topological transitivity %A L.-F. He %A Y.-H. Gao %A F.-H. Yang %J Chaos Solitons Fractals %D 2002 %V 14 %F He2002 %0 Journal Article %T Lifting and projecting continuous flows with the pseudo-orbit tracing property or the expansibility property %A L.-F. He %A G.-Z. Shan %J (Chinese); Acta Math. Appl. Sinica %D 1995 %V 18 %F He1995 %0 Journal Article %T Distal flows with pseudo-orbit tracing property %A L.-F. He %A Z.-H. Wang %J Chinese Sci. Bull. %D 1994 %V 39 %F He1994 %0 Journal Article %T Continuous semiflows with the shadowing property %A L.-F. He %A Z.-H. Wang %A H. Li %J (Chinese); Acta Math. Appl. Sinica %D 1996 %V 19 %F He1996 %0 Journal Article %T Chaos in the semi-flows and its inverse limit systems %A L.-F. He %A Z. Zhang %J Acta Math. Sci. %D 1997 %V 17 %F He1997 %0 Journal Article %T Orbital shadowing property %A B. Honary %A A. Zamani Bahabadi %J Bull. Korean Math. Soc. %D 2008 %V 45 %F Honary2008 %0 Journal Article %T A new application of the fractional logistic map %A L.-L. Huang %A D. Baleanu %A G.-C. Wu %A S.-D. Zeng %J Rom. J. Phys. %D 2016 %V 61 %F Huang2016 %0 Journal Article %T Chaos analysis of the nonlinear Duffing oscillators based on the new Adomian polynomials %A L.-L. Huang %A G.-C. Wu %A M. M. Rashidi %A W.-H. Luo %J J. Nonlinear Sci. Appl. %D 2016 %V 9 %F Huang2016 %0 Journal Article %T Pseudo-orbits and stabilities of flows %A K. Kato %J Mem. Fac. Sci. Kochi Univ. Ser. A Math. %D 1984 %V 5 %F Kato1984 %0 Journal Article %T One-parameter flows with the pseudo-orbit tracing property %A M. Komuro %J Monatsh. Math. %D 1984 %V 98 %F Komuro1984 %0 Journal Article %T Chaos and the shadowing property %A P. Kościelniak %A M. Mazur %J Topology Appl. %D 2007 %V 154 %F Kościelniak2007 %0 Journal Article %T Exploring the asymptotic average shadowing property %A M. Kulczycki %A P. Oprocha %J J. Difference Equ. Appl. %D 2010 %V 16 %F Kulczycki2010 %0 Journal Article %T Properties of dynamical systems with the asymptotic average shadowing property %A M. Kulczycki %A P. Oprocha %J Fund. Math. %D 2011 %V 212 %F Kulczycki2011 %0 Journal Article %T Investigation of the stability via shadowing property %A S.-H. Lee %A H.-J. Koh %A S.-H. Ku %J J. Inequal. Appl. %D 2009 %V 2009 %F Lee2009 %0 Journal Article %T A new method of determining chaos-parameter-region for the tent map %A C.-P. Li %J Chaos Solitons Fractals %D 2004 %V 21 %F Li2004 %0 Journal Article %T A note on shadowing with chain transitivity %A R.-S. Li %J Commun. Nonlinear Sci. Numer. Simul. %D 2012 %V 17 %F Li2012 %0 Journal Article %T A note on stronger forms of sensitivity for dynamical systems %A R.-S. Li %J Chaos Solitons Fractals %D 2012 %V 45 %F Li2012 %0 Journal Article %T A note on decay of correlation implies chaos in the sense of Devaney %A R.-S. Li %J Appl. Math. Model. %D 2015 %V 39 %F Li 2015 %0 Journal Article %T Stronger forms of sensitivity for measure-preserving maps and semiflows on probability spaces %A R.-S. Li %A Y.-M. Shi %J Abstr. Appl. Anal. %D 2014 %V 2014 %F Li2014 %0 Journal Article %T Ergodic properties of anomalous diffusion processes %A M. Magdziarz %A A. Weron %J Ann. Physics %D 2011 %V 326 %F Magdziarz2011 %0 Journal Article %T Pointwise recurrent dynamical systems with pseudo-orbit tracing property %A J.-H. Mai %J Northeast. Math. J. %D 1996 %V 12 %F Mai 1996 %0 Journal Article %T Entry and return times for semi-flows %A J. Marklof %J Nonlinearity %D 2017 %V 30 %F Marklof 2017 %0 Journal Article %T Stronger forms of sensitivity for dynamical systems %A T. K. S. Moothathu %J Nonlinearity %D 2007 %V 20 %F Moothathu2007 %0 Journal Article %T On strong ergodicity and chaoticity of systems with the asymptotic average shadowing property %A Y.-X. Niu %A S.-B. Su %J Chaos Solitons Fractals %D 2011 %V 44 %F Niu2011 %0 Journal Article %T Sets of dynamical systems with various limit shadowing properties %A S. Y. Pilyugin %J J. Dynam. Differential Equations %D 2007 %V 19 %F Pilyugin2007 %0 Journal Article %T \(C^0\) transversality and shadowing properties %A S. Y. Pilyugin %A K. Sakai %J translated from Tr. Mat. Inst. Steklova, Din. Sist. i Optim., 256 (2007), 305–319, Proc. Steklov Inst. Math. %D 2007 %V 256 %F Pilyugin2007 %0 Journal Article %T Diffeomorphisms with the average-shadowing property on two-dimensional closed manifolds %A K. Sakai %J Rocky Mountain J. Math. %D 2000 %V 3 %F Sakai 2000 %0 Journal Article %T Shadowing properties of L-hyperbolic homeomorphisms %A K. Sakai %J Topology Appl. %D 2001 %V 112 %F Sakai2001 %0 Journal Article %T Various shadowing properties for positively expansive maps %A K. Sakai %J Topology Appl. %D 2003 %V 131 %F Sakai2003 %0 Journal Article %T Differentiable dynamical systems %A S. Smale %J Bull. Amer. Math. Soc. %D 1967 %V 73 %F Smale1967 %0 Journal Article %T Stability properties of one-parameter flows %A R. F. Thomas %J Proc. London Math. Soc. %D 1982 %V 45 %F Thomas1982 %0 Journal Article %T Variations on a central limit theorem in infinite ergodic theory %A D. Thomine %J Ergodic Theory Dynam. Systems %D 2015 %V 35 %F Thomine 2015 %0 Journal Article %T Local time and first return time for periodic semi-flows %A D. Thomine %J Israel J. Math. %D 2016 %V 215 %F Thomine2016 %0 Journal Article %T Design of an image encryption scheme based on a multiple chaotic map %A X.-J. Tong %J Commun. Nonlinear Sci. Numer. Simul. %D 2013 %V 18 %F Tong2013 %0 Journal Article %T On the pseudo-orbit tracing property and its relationship to stability %A P. Walters %J The structure of attractors in dynamical systems, Proc. Conf., North Dakota State Univ., Fargo, N.D., (1977), Lecture Notes in Math., Springer, Berlin %D 1978 %V 668 %F Walters1978 %0 Book %T An introduction to ergodic theory %A P. Walters %D 1982 %I Graduate Texts in Mathematics, Springer-Verlag %C New York-Berlin %F Walters1982 %0 Journal Article %T Chaos synchronization of the discrete fractional logistic map %A G.-C. Wu %A D. Baleanu %J Signal Process. %D 2014 %V 102 %F Wu2014 %0 Journal Article %T Discrete fractional logistic map and its chaos %A G.-C. Wu %A D. Baleanu %J Nonlinear Dynam. %D 2014 %V 75 %F Wu2014 %0 Journal Article %T Chaos synchronization of fractional chaotic maps based on the stability condition %A G.-C. Wu %A D. Baleanu %A H.-P. Xie %A F.-L. Chen %J Phys. A %D 2016 %V 460 %F Wu2016 %0 Journal Article %T Nonoverlapping Schwarz waveform relaxation algorithm for a class of time-fractional heat equations %A S.-L. Wu %A G.-C. Wu %J Fund. Inform. %D 2017 %V 151 %F Wu2017 %0 Journal Article %T Two remarks on sensitive dependence of semi-dynamical systems %A X.-H. Yan %A L.-F. He %J Southeast Asian Bull. Math. %D 2008 %V 32 %F Yan2008 %0 Journal Article %T The pseudo-orbit tracing property and chaos %A R.-S. Yang %J (Chinese); Acta Math. Sinica (Chin. Ser.) %D 1996 %V 39 %F Yang 1996 %0 Journal Article %T Pseudo-orbit-tracing and completely positive entropy %A R. S. Yang %A S. L. Shen %J (Chinese); Acta Math. Sinica (Chin. Ser.) %D 1999 %V 42 %F Yang1999