Abstract
For a special class of non-injective maps on Riemannian manifolds an upper bound for the fractal dimension of invariant set in terms of singular values of the tangent map and degree of non-injectivity is given.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Belykh, V.N., Models of Discrete Systems of Phase Synchronization (in Russian), In: Systems of Phase Synchronization (eds.: V.V. Shakhgildyan and L.N. Belyustina). Moscow: Radio i Svyaz, 1982.
Biochenko, V.K., Franz, A., Leonov G.A., and Reitmann, V., Hausdorff and Fractal Dimension Estimates for Invariant Sets of Non-Injective Maps, Z. Anal. Anw., 17(1998), 207–223.
Douady, A. et Oesterlé, J., Dimension de Hausdorff des Atteracteurs, C. R. Acad. Sci. Paris Ser., A2 90(1980), 1135–1138.
Falconer, K.J., Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons, Chichester, 1990.
Mirle, A., Hausdorff Dimension Estimates for Invariant Sets ofk-1-Maps, Preprint 25/95, DFG-Schwerpunktprogramm Dynamik: Analysis, Effizients Simultation Und Ergodentheorie, 1995.
Noack, A., Reitmann, V., Hausdorff Dimension of Invariant Sets of Time-Dependent Vector Fields, ZAA, 15(1996), 457–473.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Chengqin, Q., Zuoling, Z. Fractal dimension estimates for invariant sets of non-injective maps. Anal. Theory Appl. 19, 108–114 (2003). https://doi.org/10.1007/BF02835234
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02835234