Homoclinic Loops, Heteroclinic Cycles, and Rank One Dynamics

作者：Mohapatra Anushaya^*; Ott William

来源：SIAM Journal on Applied Dynamical Systems, 2015, 14(1): 107-131.

DOI：10.1137/140995659

• heteroclinic bifurcation
• heteroclinic cycle
• homoclinic loop
• nonuniformly hyperbolic dynamics
• rank one dynamics
• saddle point shear
• SRB measure
• strange attractor

We prove that genuine nonuniformly hyperbolic dynamics emerge when flows in RN with homoclinic loops or heteroclinic cycles are subjected to certain time-periodic forcing. In particular, we establish the emergence of strange attractors and Sinai-Ruelle-Bowen (SRB) measures with strong statistical properties (central limit theorem, exponential decay of correlations, etc.). We identify and study the mechanism responsible for the nonuniform hyperbolicity: saddle point shear. Our results apply to concrete systems of interest in the biological and physical sciences, such as May-Leonard models of Lotka-Volterra dynamics.

• 出版日期2015