Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140995659 | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS |
Keywords | Field | DocType |
heteroclinic bifurcation,heteroclinic cycle,homoclinic loop,nonuniformly hyperbolic dynamics,rank one dynamics,saddle point shear,SRB measure,strange attractor | Attractor,Homoclinic bifurcation,Central limit theorem,Homoclinic orbit,Saddle point,Heteroclinic cycle,Mathematical analysis,Heteroclinic bifurcation,Mathematics,Heteroclinic orbit | Journal |
Volume | Issue | ISSN |
14 | 1 | 1536-0040 |
Citations | PageRank | References |
1 | 0.38 | 9 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anushaya Mohapatra | 1 | 1 | 0.38 |
| William Ott | 2 | 1 | 1.06 |