One-dimensional and two-dimensional dynamics of cubic maps

One - dimensional versus two - dimensional dynamics Sebastian

Hyperbolic Dynamics in Two Dimensional Maps

In this paper, we study the theory of hyperbolic dynamical systems, especially the dynamics of two-dimensional Hénon map. A remarkable fact is that the system with complicated orbit behavior (like the “horseshoe”) can be structurally stable that hyperbolicity is a necessary condition for structural stability. We discuss the horizontal and vertical slabs in a diffeomorphism on which the induced ...

Two-dimensional cubic convolution

The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a t...

Induced Maps , Markov Extensions and Invariantmeasures in One - Dimensional Dynamics

Semiconjugates of One-dimensional Maps

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