The Convergence Problem in Finite Dimensions
This core chapter concerns the convergence problem in finite dimensions. We recall that even gradient systems in two dimensions may be divergent, and we show that this phenomenon can happen even for potentials which are almost as smooth as analytic functions. Analyticity, through the Łojasiewicz gradient produces convergence of bounded trajectories, for gradient systems and some classes of gradient-like systems as well. We illustrate all the results by carefully selected examples.
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