Computer assisted proof of the existence of homoclinic tangency for the Henon map and for the forced-damped pendulum
arXiv:0905.392423 citations
Originality Incremental advance
AI Analysis
Provides a rigorous computational tool for verifying homoclinic tangency in dynamical systems, relevant to mathematicians studying chaos.
Developed a topological method for computer-assisted verification of homoclinic tangency in planar maps, successfully applied to the Henon map and forced-damped pendulum.
We present a topological method for the efficient computer assisted verification of the existence of the homoclinic tangency which unfolds generically in a one-parameter family of planar maps. The method has been applied to the Henon map and the forced damped pendulum ODE.