Related papers: Some open problems in low dimensional dynamical sy…
The purpose of this manuscript is to review my recent activity on three main research topics. The first concerns the nature of low temperature amorphous solids and their relation with the spin glass transition in a magnetic field. This is…
A technique is introduced which allows to generate -- starting from any solvable discrete-time dynamical system involving N time-dependent variables -- new, generally nonlinear, generations of discrete-time dynamical systems, also involving…
Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can…
Measuring, characterizing and modelling the slow dynamics of glassy soft matter is a great challenge, with an impact that ranges from industrial applications to fundamental issues in modern statistical physics, such as the glass transition…
We study the characterization of several distance problems for linear differential-algebraic systems with dissipative Hamiltonian structure. Since all models are only approximations of reality and data are always inaccurate, it is an…
We study linear programming and general LP-type problems in several big data (streaming and distributed) models. We mainly focus on low dimensional problems in which the number of constraints is much larger than the number of variables. Low…
We study the algebraic dynamical systems generated by triangular systems of rational functions and estimate the height growth of iterations generated by such systems. Further, using a result on the reduction modulo primes of systems of…
This expository survey is dedicated to recent developments in the area of linear dynamics. Topics include frequent hypercyclicity, $\mathcal{U}$-frequent hypercyclicity, reiterative hypercyclicity, operators of C-type, Li-Yorke and…
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…
A primitive type of two-dimensional dynamic system is introduced. It is shown that there is no decision procedure able to answer if such a dynamical system is ultimately zero.
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
We study random dynamical systems on the real line, considering each dynamical system together with the one generated by the inverse maps. We show that there is a duality between forward and inverse behaviour for such systems, splitting…
This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…
We investigate the stability of few body symmetrical dynamical systems which include four and five body symmetrical dynamical systems. Research presented in this thesis includes the following original investigations: determination of some…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
An increasing number of complex systems are now modeled as networks of coupled dynamical entities. Nonlinearity and high-dimensionality are hallmarks of the dynamics of such networks but have generally been regarded as obstacles to control.…
We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel's functional equation and to study asymptotic behavior of such semigroups.…