Variational Principles of Relative Weighted Topological Pressure

Recently, Tsukamoto (New approach to weighted topological entropy and pressure, Ergod Theory Dyn Syst 43:1004–1034, 2023) introduces a new approach to defining weighted topological entropy and pressure. Inspired by the ideas of Tsukamoto, we define the relative weighted topological entropy and pressure for factor maps and establish several variational principles. One of these results relate to a question raised by Feng and Huang (Variational principle for weighted topological pressure, J Math Pures Appl 106:411–452, 2016), namely, whether there exists a relative version of the weighted variational principle. In this paper, we try to establish such a variational principle. Furthermore, we generalize the Ledrappier and Walters type relative variational principle to the weighted version.