| Abstract: |
| Recently we developed a general theory that guarantees the existence of an orbit connecting two hyperbolic equilibria of a parametrized autonomous differential equation in $R^n$ near a suitable approximate connecting orbit generated using numerical methods. We applied this theorem to three systems in $R^3$, and, additionally, proved the existence of Sil`nikov saddle-focus chaos in each. The subject of this talk is recent work on proving the existence of Sil`nikov saddle-focus chaos in higher dimensions with an explicit example in $R^4$. |
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