The Lyapunov dimension of a nowhere differentiable attracting torus
Open Access
- 1 June 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 4 (2) , 261-281
- https://doi.org/10.1017/s0143385700002431
Abstract
The fractal dimension of an attracting torus Tk in × Tk is shown to be almost always equal to the Lyapunov dimension as predicted by a previous conjecture. The cases studied here can have several Lyapunov numbers greater than 1 and several less than 1Keywords
This publication has 12 references indexed in Scilit:
- Fat baker's transformationsErgodic Theory and Dynamical Systems, 1984
- The dimension of chaotic attractorsPhysica D: Nonlinear Phenomena, 1983
- Some relations between dimension and Lyapounov exponentsCommunications in Mathematical Physics, 1981
- On the Weierstrass-Mandelbrot fractal functionProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1980
- Numerical solution of a generalized eigenvalue problem for even mappingsLecture Notes in Mathematics, 1979
- On a theorem of AnosovJournal of Differential Equations, 1969
- On Curves of Fractional DimensionsJournal of the London Mathematical Society, 1945
- Sets of Fractional Dimensions (V): on Dimensional Numbers of Some Continuous CurvesJournal of the London Mathematical Society, 1937
- Weierstrass's Non-Differentiable FunctionTransactions of the American Mathematical Society, 1916
- Weierstrass’s non-differentiable functionTransactions of the American Mathematical Society, 1916