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High-order homoclinic tangencies of corank 2
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems , First View
- Published online by Cambridge University Press:
- 29 August 2025, pp. 1-45
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- Article
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We prove that in the space of
$C^r$ maps 
$(r=2,\ldots ,\infty ,\omega )$ of a smooth manifold of dimension at least 4, there exist open regions where maps with infinitely many corank-2 homoclinic tangencies of all orders are dense. The result is applied to show the existence of maps with universal two-dimensional dynamics, that is, maps whose iterations approximate the dynamics of every map of a two-dimensional disk with an arbitrarily good accuracy. We show that maps with universal two-dimensional dynamics are 
$C^r$-generic in the regions under consideration.
Examples of Lorenz-like Attractors in Hénon-likeMaps
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- Journal:
- Mathematical Modelling of Natural Phenomena / Volume 8 / Issue 5 / 2013
- Published online by Cambridge University Press:
- 17 September 2013, pp. 48-70
- Print publication:
- 2013
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- Article
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