2021/08/09 by Tsukamoto, Masaki
#37A35 #37B40 #37C45 #37D35 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2108.03795
Motivated by fractal geometry of self-affine carpets and sponges, Feng--Huang (2016) introduced weighted topological entropy and pressure for factor maps between dynamical systems, and proved variational principles for them. We introduce a new approach to this theory. Our new definitions of weighted topological entropy and pressure are very different from the original definitions of Feng--Huang. The equivalence of the two definitions seems highly nontrivial. Their equivalence can be seen as a generalization of the dimension formula for the Bedford--McMullen carpet in purely topological terms.