Abstract
Chaotic dynamics arises when the unstable manifold of a hyperbolic equilibrium point changes its twist type along a homoclinic orbit as some generic parameter is varied. Such bifurcation points occur naturally in singularly perturbed systems. Some quotient symbolic systems induced from the Bernoulli symbolic system on two symbols are proved to be characteristic for this new mechanism of chaos generation. Combination of geometrical and analytical methods is proved to be more fruitful.
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Deng, B. Homoclinic twisting bifurcations and cusp horseshoe maps. J Dyn Diff Equat 5, 417–467 (1993). https://doi.org/10.1007/BF01053531
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DOI: https://doi.org/10.1007/BF01053531
Key words
- Strong inclination property
- neutrally twisted homoclinic orbits
- cusp horseshoe maps
- quotient symbolic systems
- singular perturbations