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Volumn 17, Issue 1, 1998, Pages 207-223

Hausdorff and fractal dimension estimates for invariant sets of non-injective maps

Author keywords

Fractal dimension estimates; Hausdorff dimension estimates; Non injective maps; Singular values; Tangent map

Indexed keywords


EID: 21944432516     PISSN: 02322064     EISSN: None     Source Type: Journal    
DOI: 10.4171/ZAA/816     Document Type: Article
Times cited : (11)

References (15)
  • 1
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    • Models of discrete systems of phase synchronization
    • (eds.: V. V. Shakhgil'dyan and L. N. Belyustina). Moscow: Radio i Svyaz'
    • Belykh, V. N.: Models of discrete systems of phase synchronization (in Russian). In: Systems of phase synchronization (eds.: V. V. Shakhgil'dyan and L. N. Belyustina). Moscow: Radio i Svyaz' 1982.
    • (1982) Systems of Phase Synchronization
    • Belykh, V.N.1
  • 3
    • 0142146207 scopus 로고
    • Local Lyapunov exponents and a local estimate of Hausdorff dimension
    • Eden, A.: Local Lyapunov exponents and a local estimate of Hausdorff dimension. Math. Modelling and Num. Anal. 23 (1989), 405-413.
    • (1989) Math. Modelling and Num. Anal. , vol.23 , pp. 405-413
    • Eden, A.1
  • 6
    • 34250238889 scopus 로고
    • Some relations between dimension and Lyapunov exponents
    • Ledrappier, F.: Some relations between dimension and Lyapunov exponents. Commun. Math. Phys. 81 (1981), 229-283.
    • (1981) Commun. Math. Phys. , vol.81 , pp. 229-283
    • Ledrappier, F.1
  • 7
    • 0001713320 scopus 로고
    • Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors
    • Leonov, G. A. and V. A. Doichenko: Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors. Acta Appl. Math. 26 (1992), 1-60.
    • (1992) Acta Appl. Math. , vol.26 , pp. 1-60
    • Leonov, G.A.1    Doichenko, V.A.2
  • 9
    • 26444525556 scopus 로고
    • Preprint 25/95, DFG-Schwerpunktprogramm "Dynamik: Analysis, effiziente Simulation und Ergodentheorie"
    • Mirle, A.: Hausdorff dimension estimates for invariant sets of k - 1-maps. Preprint 25/95, DFG-Schwerpunktprogramm "Dynamik: Analysis, effiziente Simulation und Ergodentheorie" 1995.
    • (1995) Hausdorff Dimension Estimates for Invariant Sets of k - 1-maps
    • Mirle, A.1
  • 10
    • 21344466746 scopus 로고    scopus 로고
    • Hausdorff dimension of invariant sets of time-dependent vector fields
    • Noack, A. and V. Reitmann: Hausdorff dimension of invariant sets of time-dependent vector fields. Z. Anal. Anw. 15 (1996), 457-473.
    • (1996) Z. Anal. Anw. , vol.15 , pp. 457-473
    • Noack, A.1    Reitmann, V.2
  • 11
    • 85157091241 scopus 로고    scopus 로고
    • Hausdorff dimension estimates for invariant sets of piecewise smooth maps
    • to appear
    • Reitmann, V. and U. Schnabel: Hausdorff dimension estimates for invariant sets of piecewise smooth maps. Z. Ang. Math. Mech. (ZAMM) (to appear).
    • Z. Ang. Math. Mech. (ZAMM)
    • Reitmann, V.1    Schnabel, U.2
  • 12
    • 0003310263 scopus 로고
    • Hausdorff dimension for non-invertible maps
    • Simon, K.: Hausdorff dimension for non-invertible maps. Ergod. theory & Dyn. Sys. 13 (1993), 199-212.
    • (1993) Ergod. Theory & Dyn. Sys. , vol.13 , pp. 199-212
    • Simon, K.1
  • 14
    • 0001746066 scopus 로고
    • Entropy and the Hausdorff dimension for infinite-dimensional dynamical systems
    • Thieullen, P.: Entropy and the Hausdorff dimension for infinite-dimensional dynamical systems. J. Dyn. Dili. Equ. 4 (1992), 127-159.
    • (1992) J. Dyn. Dili. Equ. , vol.4 , pp. 127-159
    • Thieullen, P.1
  • 15
    • 0027659460 scopus 로고
    • A note on Kaplan-Yorke-type estimates on the fractal dimension of chaotic attractors
    • Zhi-Min Chen: A note on Kaplan-Yorke-type estimates on the fractal dimension of chaotic attractors. Chaos, Solitons & Fractals 3 (1993), 575-582.
    • (1993) Chaos, Solitons & Fractals , vol.3 , pp. 575-582
    • Chen, Z.-M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.