2015/01/31 by Hiroki Takahasi
Mathematics · #math.DS #msc:37D25 #msc:37E30 #msc:37G25
published as Dynamical Systems: An International Journal, 31 (2016) 41-59 · 2 figures, 17 pages. arXiv admin note: substantial text overlap with arXiv:1405.1813
arxiv created 2015/01/31 · arxiv updated 2016/03/03
We effect a multifractal analysis for a strongly dissipative Hénon-like map at the first bifurcation parameter at which the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set. We decompose the set of non wandering points on the unstable manifold into level sets of Birkhoff averages of continuous functions, and derive a formula for the Hausdorff dimension of the level sets in terms of the entropy and unstable Lyapunov exponent of invariant probability measures.