Abstract
For a continuous transformation f of a compact metric space (X, d) and any continuous function φ on X we consider sets of the form
Kα = {x ∈ X : lim n→∞ 1/n n−1Σi=0 φ(f^i(x)) = α}, α ∈ R.
For transformations satisfying the specification property we prove the following Variational Principle
htop(f, Kα) = sup(hµ(f): µ is invariant and ∫φdµ = α),
where htop(f, ·) is the topological entropy of non-compact sets. Using this result we are able to obtain a complete description of the multifractal spectrum for Lyapunov exponents of the so-called Manneville–Pomeau map, which is an interval map with an indifferent fixed point.
We also consider multi-dimensional multifractal spectra and establish a contraction principle.
Original language | English |
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Pages (from-to) | 317-348 |
Number of pages | 32 |
Journal | Ergodic Theory and Dynamical Systems |
Volume | 23 |
DOIs | |
Publication status | Published - Feb-2003 |
Keywords
- MULTIFRACTAL ANALYSIS
- MAPS
- INTERMITTENCY
- ROTATION
- STATES
- SPACE