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...As with dimension spectra, the fully non-uniform case of multimodal maps cannot be treated with the results in this paper. The Lyapunov spectrum for multimodal maps has been studied by Iommi and Todd =-=[IT09a]-=- using inducing schemes and thermodynamic results. For non-conformal maps, life is again more difficult; some results on the entropy spectrum for Lyapunov exponents are given in [BG06]. 3.3. Results f...

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...fined is the geometric pressure function of f . It is closely related to several multifractal spectra and large deviation rate functions associated with f , see for example [BMS03, Lemma 2], [GPR10], =-=[IT11]-=-, [KN92, Theorems 1.2 and 1.3], [PRL11, Appendix B], and references therein. We exhibit a transitive quadratic map whose geometric pressure function behaves, for some constants A > 0 and χ > 0 and for...

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...estricted t) and [IT1] (multimodal case, general t) that there is an equilibrium state µt corresponding to ϕt. The relation between these measures, the pressure and the Lyapunov spectrum was shown in =-=[IT2]-=-. The classical Bowen formula in the uniformly expanding case, see for example [Ra], states that the Hausdorff Date: February 19, 2014. MD was partially supported by NSF grant DMS 1101572. MT was part...

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...31], and a complete picture is emerging. For one-dimensional maps, several progresses have been made to relax these assumptions: allowing parabolic fixed points [11, 15, 18]; allowing critical points =-=[7, 8, 12, 14, 22]-=-. Nevertheless, litte is known on higher dimensional systems. Indeed, one can mention interesting recent developments [1, 28] on two-dimensional maps with parabolic fixed points. In these papers, howe...

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...g by χinf the infimum of exponents of f -invariant probability measures on K, we obtain that χ(x) ≥ χinf for every x ∈ K for which χ(x) exists and is different from −∞. This was conjectured before in =-=[14, 15]-=-2. Moreover, in the case that K = Î, f is non-exceptional, and has no indifferent periodic orbits in K, we conclude that χ(x)] ≥ χinf provided χ(x) > 0. Here χ(x)] denotes a certain non-negative aver...