Related papers: Linearisable Mappings and the Low-Growth Criterion
We present an integrability criterion for rational mappings based on two requirements. First, that a given point should have a unique preimage under the mapping and, second, that the spontaneously appearing singularities be confined to a…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity properties of the original, has proven crucial in our…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential…
We describe the various types of singularities that can arise for second order rational mappings and we discuss the historical and present-day, practical, role the singularity confinement property plays as an integrability detector. In…
In this paper we give an explanation of a number of observations relating to degree growth of birational mappings of the plane and their deautonomisation by singularity confinement. These observations are of a link between two a priori…
We study the growth of degrees in many autonomous and non-autonomous lattice equations defined by quad rules with corner boundary values, some of which are known to be integrable by other characterisations. Subject to an enabling…
We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic…
This article is concerned with pointwise growth and spreading speeds in systems of parabolic partial differential equations. Several criteria exist for quantifying pointwise growth rates. These include the location in the complex plane of…
Integrability of the differential constraints arising from the singularity analysis of two (1+1)-dimensional second-order evolution equations is studied. Two nonlinear ordinary differential equations are obtained in this way, which are…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…
The intrinsic nature of a problem usually suggests a first suitable method to deal with it. Unfortunately, the apparent ease of application of these initial approaches may make their possible flaws seem to be inherent to the problem and…
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one…
In [1], it is established that a convergent observer with an infinite gain margin can be designed for a given nonlinear system when a Riemannian metric showing that the system is differentially detectable (i.e., the Lie derivative of the…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…