Non-algebraic attractors on $\mathbf{P}^k$

Feng Rong

doi:10.3934/dcds.2012.32.977

Article Contents

2012, Volume 32, Issue 3: 977-989. Doi: 10.3934/dcds.2012.32.977

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Non-algebraic attractors on $\mathbf{P}^k$

Feng Rong^1,

1.
Department of Mathematics, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240

Received: August 31, 2010

Revised: April 30, 2011

Published: February 2012

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Abstract

We show that special perturbations of a particular holomorphic map on $\mathbf{P}^k$ give us examples of maps that possess chaotic non-algebraic attractors. Furthermore, we study the dynamics of the maps on the attractors. In particular, we construct invariant hyperbolic measures supported on the attractors with nice dynamical properties.

Keywords:

Attractors,
hyperbolic measures.

Mathematics Subject Classification: Primary 32H50; Secondary 37C70.

Citation:

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