相关论文: Studying discrete dynamical systems trough differe…
We describe a canonical procedure for associating to any (germ of) holomorphic self-map f of C^n fixing the origin such that df_O is invertible and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p from M to C^n, a…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
Differential calculus on Euclidean spaces has many generalisations. In particular, on a set $X$, a diffeological structure is given by maps from open subsets of Euclidean spaces to $X$, a differential structure is given by maps from $X$ to…
In the presence of a chemically active particle, a nearby chemically inert particle can respond to a concentration gradient and move by diffusiophoresis. The nature of the motion is studied for two cases: first, a fixed reactive sphere and…
Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…
Temporally evolving systems are typically modeled by dynamic equations. A key challenge in accurate modeling is understanding the causal relationships between subsystems, as well as identifying the presence and influence of unobserved…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
Let $X_0$ be a smooth projective threefold which is Fano or which has Picard number $1$. Let $\pi :X\rightarrow X_0$ be a finite composition of blowups along smooth centers. We show that for "almost all" of such $X$, if $f\in Aut(X)$ then…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
Differential-difference equation $\frac{d}{dx}t(n+1,x)=f(x,t(n,x),t(n+1,x),\frac{d}{dx}t(n,x))$ with unknown $t(n,x)$ depending on continuous and discrete variables $x$ and $n$ is studied. We call an equation of such kind Darboux…
We show how fundamental ideas from signal processing, multiscale theory and wavelets may be applied to non-linear dynamics. The problems from dynamics include iterated function systems (IFS), dynamical systems based on substitution such as…
The dynamical properties of classical fluids at pico-liter scale attract experimentally and theoretically much attention in the soft-matter and biophysics communities, due to the appearance of the microfluidics, also called 'lab-on-a-chip',…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
In our previous paper [N. Tsutsumi, K. Nakai and Y. Saiki, Chaos 32, 091101 (2022)], we proposed a method for constructing a system of differential equations of chaotic behavior from only observable deterministic time series, which we call…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
We study initial value problems having dynamics ruled by discontinuous ordinary differential equations with the property of possessing a unique solution. We identify a precise class of such systems that we call solvable intitial value…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…