Continuous time evolution from iterated maps and Carleman linearization

Explicit Error Bounds for Carleman Linearization

We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides. This transformation provides an approximate linearization in a higher-dimensional space through the exact embedding of polynomial nonlinearities into an infinite-dimensional linear system, which is then truncated to obtain a finite-dimensional representation with an a...

On Carleman Linearization of Linearly Observable Polynomial Systems

Carleman linearization is used to transform a polynomial control system with output, defined on n-dimensional space, into a linear or bilinear system evolving in the space of infinite sequences. Such a system is described by infinite matrices with special properties. Linear observability of the original system is studied. It means that all coordinate functions can be expressed as linear combina...

From the Cover : Searching with iterated maps

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Searching with iterated maps.

In many problems that require extensive searching, the solution can be described as satisfying two competing constraints, where satisfying each independently does not pose a challenge. As an alternative to tree-based and stochastic searching, for these problems we propose using an iterated map built from the projections to the two constraint sets. Algorithms of this kind have been the method of...

Continuous Iterated Density Estimation