Discrete Dynamical Systems

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Degenerate Feedback Loops in Recommender Systems (2019, background): “Sufﬁcient (but not necessary) conditions for global stability are given by the following theorem (Galor, 2007): then a stationary equilibrium of the difference equation y t +1 = g ( y t ) exists and is unique and globally (asymptotically) stable.”
Interaction Matters: A Note on Non-asymptotic Local Convergence of Generative Adversarial Networks (2018, background): “is better than converging/oscillating/escaping an unstable local solution, in terms of distribution learning. Recent progress by Daskalakis and Panageas [2018b,a] employs the stable manifold Theorem [Galor, 2007] to show that certain dynamics avoid unstable local solutions (barring initialization in”
The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization (2018, unknown): “Proposition 1.4 (e.g. [8]) .”
On Solving Minimax Optimization Locally: A Follow-the-Ridge Approach (2019, background): “It is known that strict stability implies local convergence ( e.g. , see Galor (2007)).”