A survey on macroeconomic data and trends in the Eurozone and a control dashboard model based on the KAM and Nekhoroshev theorems and the Hénon attractor

Starting from the examination of the main macroeconomic parameters that have characterized the structure of the Eurozone in the last decade – and their systemization – our aim was to apply a model suitable for describing its dynamics. In particular, the Kolmogorov-Arnold-Moser theorem was adapted to the question, up to low level perturbations caused by negative economic conditions, the first symptoms of financial or exogenous crises, and other turbulence affecting the economy. We then applied Nekhoroshev's theorem to represent the phenomena characterized by the occurrence of stronger resonance as well as the reactions of the system to the control and recovery measures implemented by the ECB Governing Council. The goal of the paper is to propose the adoption of a systemic stability planning and control dashboard – also suitable for the support and stimulation of growth cycles – with attention to optimal performance, which can be identified in compliance with (or restoration of) the macroeconomic trajectories determined in the model by the Hénon Attractor. The proposed scheme may find useful application – both for evaluation and operational purposes – in the current period, characterized by the complex and compromised scenario brought about by the SARS-COVID2 pandemic emergency, which has obviously imposed structured measures to support the economy.