IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v33y2007i1p76-86.html
   My bibliography  Save this article

Topological entropy and chaos for maps induced on hyperspaces

Author

Listed:
  • Kwietniak, Dominik
  • Oprocha, Piotr

Abstract

If f is a continuous selfmap of a compact metric space X then by the induced map we mean the map f¯ defined on the space of all nonempty closed subsets of X by f¯(K)=f(K).

Suggested Citation

  • Kwietniak, Dominik & Oprocha, Piotr, 2007. "Topological entropy and chaos for maps induced on hyperspaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 76-86.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:76-86
    DOI: 10.1016/j.chaos.2005.12.033
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906000415
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.12.033?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Gengrong & Zeng, Fanping & Liu, Xinhe, 2006. "Devaney’s chaotic on induced maps of hyperspace," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 471-475.
    2. Fedeli, Alessandro, 2005. "On chaotic set-valued discrete dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1381-1384.
    3. Román-Flores, Heriberto & Chalco-Cano, Y., 2005. "Robinson’s chaos in set-valued discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 33-42.
    4. Peris, Alfredo, 2005. "Set-valued discrete chaos," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 19-23.
    5. Gu, Rongbao & Guo, Wenjing, 2006. "On mixing property in set-valued discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 747-754.
    6. Banks, John, 2005. "Chaos for induced hyperspace maps," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 681-685.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhu, Wanting & Sun, Kehui & He, Shaobo & Wang, Huihai & Liu, Wenhao, 2023. "A class of m-dimension grid multi-cavity hyperchaotic maps and its application," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Fedeli, Alessandro, 2009. "On two notions of topological entropy for noncompact spaces," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 432-435.
    3. Andres, Jan, 2020. "Chaos for multivalued maps and induced hyperspace maps," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Li, Risong, 2012. "A note on stronger forms of sensitivity for dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 753-758.
    5. Liu, Heng & Liao, Gongfu & Hou, Bingzhe, 2009. "The set-valued mapping induced by a non-minimal transitive system is Li–Yorke chaotic," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 826-830.
    6. Daghar, Aymen & Naghmouchi, Issam, 2022. "Entropy of induced maps of regular curves homeomorphisms," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Román-Flores, H. & Chalco-Cano, Y. & Silva, G.N. & Kupka, Jiří, 2011. "On turbulent, erratic and other dynamical properties of Zadeh’s extensions," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 990-994.
    8. Wang, Yangeng & Wei, Guo & Campbell, William H. & Bourquin, Steven, 2009. "A framework of induced hyperspace dynamical systems equipped with the hit-or-miss topology," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1708-1717.
    9. Andres, Jan & Ludvík, Pavel, 2022. "Topological entropy of multivalued maps in topological spaces and hyperspaces," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    10. Liu, Lei & Wang, Yangeng & Wei, Guo, 2009. "Topological entropy of continuous functions on topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 417-427.
    11. Fu, Heman & Xing, Zhitao, 2012. "Mixing properties of set-valued maps on hyperspaces via Furstenberg families," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 439-443.
    12. Hou, Bingzhe & Liao, Gongfu & Liu, Heng, 2008. "Sensitivity for set-valued maps induced by M-systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1075-1080.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fu, Heman & Xing, Zhitao, 2012. "Mixing properties of set-valued maps on hyperspaces via Furstenberg families," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 439-443.
    2. Liu, Heng & Liao, Gongfu & Hou, Bingzhe, 2009. "The set-valued mapping induced by a non-minimal transitive system is Li–Yorke chaotic," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 826-830.
    3. Hou, Bingzhe & Liao, Gongfu & Liu, Heng, 2008. "Sensitivity for set-valued maps induced by M-systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1075-1080.
    4. Cánovas Peña, Jose S. & López, Gabriel Soler, 2006. "Topological entropy for induced hyperspace maps," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 979-982.
    5. Andres, Jan, 2020. "Chaos for multivalued maps and induced hyperspace maps," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    6. Wang, Yangeng & Wei, Guo & Campbell, William H. & Bourquin, Steven, 2009. "A framework of induced hyperspace dynamical systems equipped with the hit-or-miss topology," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1708-1717.
    7. Román-Flores, H. & Chalco-Cano, Y., 2008. "Some chaotic properties of Zadeh’s extensions," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 452-459.
    8. Daniel Jardón & Iván Sánchez & Manuel Sanchis, 2020. "Transitivity in Fuzzy Hyperspaces," Mathematics, MDPI, vol. 8(11), pages 1-9, October.
    9. Félix Martínez-Giménez & Alfred Peris & Francisco Rodenas, 2021. "Chaos on Fuzzy Dynamical Systems," Mathematics, MDPI, vol. 9(20), pages 1-11, October.
    10. Sánchez, Iván & Sanchis, Manuel & Villanueva, Hugo, 2017. "Chaos in hyperspaces of nonautonomous discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 68-74.
    11. Li, Risong, 2012. "A note on stronger forms of sensitivity for dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 753-758.
    12. Llorens-Fuster, Enrique & Petruşel, Adrian & Yao, Jen-Chih, 2009. "Iterated function systems and well-posedness," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1561-1568.
    13. Román-Flores, H. & Chalco-Cano, Y. & Silva, G.N. & Kupka, Jiří, 2011. "On turbulent, erratic and other dynamical properties of Zadeh’s extensions," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 990-994.
    14. Jan Andres, 2020. "Multiple Periodic Solutions and Fractal Attractors of Differential Equations with n -Valued Impulses," Mathematics, MDPI, vol. 8(10), pages 1-21, October.
    15. Chalco-Cano, Y. & Román-Flores, H., 2008. "On new solutions of fuzzy differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 112-119.
    16. Daghar, Aymen & Naghmouchi, Issam, 2022. "Entropy of induced maps of regular curves homeomorphisms," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    17. Camargo, Javier & Rincón, Michael & Uzcátegui, Carlos, 2019. "Equicontinuity of maps on dendrites," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 1-6.
    18. Yilmaz, Yilmaz, 2009. "Fréchet differentiation of nonlinear operators between fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 473-484.
    19. Peris, Alfredo, 2005. "Set-valued discrete chaos," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 19-23.
    20. Zhang, Gengrong & Zeng, Fanping & Liu, Xinhe, 2006. "Devaney’s chaotic on induced maps of hyperspace," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 471-475.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:33:y:2007:i:1:p:76-86. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.