It often arises near transverse homoclinic points, as in the Smale horseshoe. A Poincar?section or first-return map for this type of dynamics will exhibit a fractal structure. In examples such as the logistic map, as a parameter is increased a sequence of period doubling bifurcations characterized by the Feigenbaum constant leads to its onset. It is characterized by positive Lyapunov exponents, meaning that small errors in initial data grow quickly and make practical long-term predictions impossible. Devaney specified t
It often arises near transverse homoclinic points, as in the Smale horseshoe. A Poincar?section or first-return map for this type of dynamics will exhibit a fractal structure. In examples such as the logistic map, as a parameter is increased a sequence of period doubling bifurcations characterized by the Feigenbaum constant leads to its onset. It is characterized by positive Lyapunov exponents, meaning that small errors in initial data grow quickly and make practical long-term predictions impossible. Devaney specified three requirements for it: topological transitivity, dense periodic orbits, and sensitivity to initial conditions. For 10 points, what is this physical phenomenon, exemplified by the weather, in which a deterministic system exhibits apparently random behavior?
It often arises near transverse homoclinic points, as in the Smale horseshoe.
chaos