Nonlinear thermodynamic formalism through the lens of rotation theory (Q6614212)

The nonlinear thermodynamic formalism in [\textit{J. Buzzi} et al., Ann. Henri Lebesgue 6, 1429--1477 (2023; Zbl 1545.37033)] introduces a nonlinear topological pressure \(\Pi^F_{\mathrm{top}}(\Phi)\) of a vector valued continuous potential function \(\Phi\colon X\to\mathbb R^m\) (with respect to a dynamical system \((X,T)\)) considering a multivariable continuous nonlinearity function \(F\colon\mathbb R^m\to\mathbb R\) instead of just one single continuous potential function. \N\NThe present work presents a variational principle for this nonlinear topological pressure,\N\[\N\Pi^F_{\mathrm{top}}(\Phi) = \sup_{w\in\mathrm{Rot}_{\mathrm{Pt}}(\Phi)}\{h(w)+F(w)\},\N\]\Nwhere \(h(\cdot)\) denotes the localized topological entropy and \(\mathrm{Rot}_{\mathrm{Pt}}(\Phi)\) denotes the pointwise rotation et of \(\Phi\). It also provides an alternative proof of the generalized variational principle provided in [loc. cit.] which is based on the above result and tools from rotation theory.