Three invariants of strange attractors derived through hypergeometric entropy

A new description of strange attractor systems through three geometrical and dynamical invariants is provided. They are the correlation dimension ($\mathcal{D}$) entropy ($\mathcal{K}$), both having attracted attention over past decades, a invariant called concentration ($\mathcal{A}$) introduced in present study. The defined as normalised mean distance between reconstruction vectors, evaluated by underlying probability measure on infinite-dimensional embedding space. These determine scaling behaviour system's R\'{e}nyi-type extended entropy, modelled Kummer's confluent hypergeometric function, with respect to gauge parameter ($\rho$) coupled vectors. function reproduces known behaviours $\mathcal{D}$ $\mathcal{K}$ 'microscopic' limit $\rho\to\infty$ while exhibiting $\mathcal{A}$ other, 'macroscopic' $\rho\to 0$. estimated simultaneously via nonlinear regression analysis without needing separate estimations for each invariant. proposed method verified simulations discrete continuous systems.