Non-expansive Hénon maps (Q1104622)

The author studies the map of the plane \(f(x,y)=(y,y^ 2-\delta x- \alpha)\), \(\alpha\),\(\delta\)-parameters, being a normal form of the Hénon map. Let h(f) be the topological entropy of f. It is shown that 1) h is continuous in \(\alpha\),\(\delta\) and for each fixed \(\delta\) it takes on all values in [0, log 2]; 2) there exists a countable set \(\Sigma_{\delta}\) such that the map f can be expansive only if \(h(f)\in \Sigma_{\delta}\).