sequence of letters. A heteroclinic orbit is then the joining of two distinct periodic orbits. It may be written as where is a sequence of symbols of length k, (of course, ), and is another sequence of symbols, of length m (likewise, ). The notation simply denotes the repetition of p an infinite number of times. Thus, a heteroclinic orbit can be understood as the transition from one periodic orbit to another. By contrast, a homoclinic orbit can be written as with the intermediate sequence being non-empty, and, of course, not being p, as otherwise, the orbit would simply be . See also Heteroclinic orbit Homoclinic bifurcation References John Guckenheimer and Philip Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences Vol. 42), Springer External links Homoclinic orbits in Henon map with Java applets and comments Dynamical systems