American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Exponential stability in non-autonomous delayed equations with applications to neural networks
  • DCDS Home
  • This Issue
  • Next Article
    Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations
March  2007, 18(2&3): 499-515. doi: 10.3934/dcds.2007.18.499

Continuous dependence of attractors on parameters of non-autonomous dynamical systems and infinite iterated function systems

David Cheban 1, and  Cristiana Mammana 2,

1. 

State University of Moldova, Department of Mathematics and Informatics, A. Mateevich Street 60, MD–2009 Chişinău
2. 

Institute of Economics and Finances, University of Macerata, str. Crescimbeni 14, I–62100 Macerata, Italy

Received  February 2006 Revised  July 2006 Published  March 2007

The paper is dedicated to the study of the problem of continuous dependence of compact global attractors on parameters of non-autonomous dynamical systems and infinite iterated function systems (IIFS). We prove that if a family of non-autonomous dynamical systems ‹$(X,\mathbb T_1,\pi_{\lambda}),(Y,\mathbb T_{2},\sigma),h $›depending on parameter $\lambda\in\Lambda$ is uniformly contracting (in the generalized sense), then each system of this family admits a compact global attractor $J^{\lambda}$ and the mapping $\lambda \to J^{\lambda}$ is continuous with respect to the Hausdorff metric. As an application we give a generalization of well known Theorem of Bransley concerning the continuous dependence of fractals on parameters.
Keywords: Global attractor; non-autonomous dynamical system; infinite iterated functions systems..
Mathematics Subject Classification: 37B25, 37B55, 39A11, 39C10, 39C5.
Citation: David Cheban, Cristiana Mammana. Continuous dependence of attractors on parameters of non-autonomous dynamical systems and infinite iterated function systems. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 499-515. doi: 10.3934/dcds.2007.18.499
[1]

Tomás Caraballo, David Cheban. On the structure of the global attractor for infinite-dimensional non-autonomous dynamical systems with weak convergence. Communications on Pure & Applied Analysis, 2013, 12 (1) : 281-302. doi: 10.3934/cpaa.2013.12.281
[2]

Tomás Caraballo, David Cheban. On the structure of the global attractor for non-autonomous dynamical systems with weak convergence. Communications on Pure & Applied Analysis, 2012, 11 (2) : 809-828. doi: 10.3934/cpaa.2012.11.809
[3]

Alexandre N. Carvalho, José A. Langa, James C. Robinson. Non-autonomous dynamical systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (3) : 703-747. doi: 10.3934/dcdsb.2015.20.703
[4]

Michael Zgurovsky, Mark Gluzman, Nataliia Gorban, Pavlo Kasyanov, Liliia Paliichuk, Olha Khomenko. Uniform global attractors for non-autonomous dissipative dynamical systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 2053-2065. doi: 10.3934/dcdsb.2017120
[5]

Alexandre N. Carvalho, José A. Langa, James C. Robinson. Forwards dynamics of non-autonomous dynamical systems: Driving semigroups without backwards uniqueness and structure of the attractor. Communications on Pure & Applied Analysis, 2020, 19 (4) : 1997-2013. doi: 10.3934/cpaa.2020088
[6]

Rodrigo Samprogna, Tomás Caraballo. Pullback attractor for a dynamic boundary non-autonomous problem with Infinite Delay. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 509-523. doi: 10.3934/dcdsb.2017195
[7]

Noriaki Yamazaki. Global attractors for non-autonomous multivalued dynamical systems associated with double obstacle problems. Conference Publications, 2003, 2003 (Special) : 935-944. doi: 10.3934/proc.2003.2003.935
[8]

Xinyuan Liao, Caidi Zhao, Shengfan Zhou. Compact uniform attractors for dissipative non-autonomous lattice dynamical systems. Communications on Pure & Applied Analysis, 2007, 6 (4) : 1087-1111. doi: 10.3934/cpaa.2007.6.1087
[9]

Grzegorz Łukaszewicz, James C. Robinson. Invariant measures for non-autonomous dissipative dynamical systems. Discrete & Continuous Dynamical Systems, 2014, 34 (10) : 4211-4222. doi: 10.3934/dcds.2014.34.4211
[10]

Michael Dellnitz, Christian Horenkamp. The efficient approximation of coherent pairs in non-autonomous dynamical systems. Discrete & Continuous Dynamical Systems, 2012, 32 (9) : 3029-3042. doi: 10.3934/dcds.2012.32.3029
[11]

Wen Tan. The regularity of pullback attractor for a non-autonomous p-Laplacian equation with dynamical boundary condition. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 529-546. doi: 10.3934/dcdsb.2018194
[12]

V. V. Chepyzhov, M. I. Vishik, W. L. Wendland. On non-autonomous sine-Gordon type equations with a simple global attractor and some averaging. Discrete & Continuous Dynamical Systems, 2005, 12 (1) : 27-38. doi: 10.3934/dcds.2005.12.27
[13]

T. Tachim Medjo. Non-autonomous 3D primitive equations with oscillating external force and its global attractor. Discrete & Continuous Dynamical Systems, 2012, 32 (1) : 265-291. doi: 10.3934/dcds.2012.32.265
[14]

Birgit Jacob, Hafida Laasri. Well-posedness of infinite-dimensional non-autonomous passive boundary control systems. Evolution Equations & Control Theory, 2021, 10 (2) : 385-409. doi: 10.3934/eect.2020072
[15]

Xiaoyue Li, Xuerong Mao. Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation. Discrete & Continuous Dynamical Systems, 2009, 24 (2) : 523-545. doi: 10.3934/dcds.2009.24.523
[16]

Emma D'Aniello, Saber Elaydi. The structure of $ \omega $-limit sets of asymptotically non-autonomous discrete dynamical systems. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 903-915. doi: 10.3934/dcdsb.2019195
[17]

Mikhail B. Sevryuk. Invariant tori in quasi-periodic non-autonomous dynamical systems via Herman's method. Discrete & Continuous Dynamical Systems, 2007, 18 (2&3) : 569-595. doi: 10.3934/dcds.2007.18.569
[18]

Bixiang Wang. Multivalued non-autonomous random dynamical systems for wave equations without uniqueness. Discrete & Continuous Dynamical Systems - B, 2017, 22 (5) : 2011-2051. doi: 10.3934/dcdsb.2017119
[19]

Radosław Czaja. Pullback attractors via quasi-stability for non-autonomous lattice dynamical systems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021276
[20]

Chunyou Sun, Daomin Cao, Jinqiao Duan. Non-autonomous wave dynamics with memory --- asymptotic regularity and uniform attractor. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 743-761. doi: 10.3934/dcdsb.2008.9.743

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (39)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy