Search for "Dynamical Systems" in article titles:

1. Dynamical systems: A dynamical system is a rule for time evolution on a state space. A dynamical system consists of an abstract phase space or state space, whose coordinates describe the state at any instant, and a dynamical rule that specifies the ... [100%] 2021-12-24 [Dynamical Systems]
2. Stochastic dynamical systems: A stochastic dynamical system is a dynamical system subjected to the effects of noise. Such effects of fluctuations have been of interest for over a century since the seminal work of Einstein (1905). [81%] 2021-12-24 [Dynamical Systems] [Noise]...
3. Dynamical systems theory: Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. (Area of mathematics used to describe the behavior of complex dynamical systems) [81%] 2023-12-12 [Dynamical systems] [Complex systems theory]...
4. Minimal dynamical systems: Minimal systems are natural generalizations of periodic orbits, and they are analogues of ergodic measures in topological dynamics. They were defined by G. [81%] 2021-12-24 [Mappings] [Topological Dynamics]...
5. Equivariant dynamical systems: Equivariant dynamical systems are dynamical systems that have symmetries. A symmetry of a dynamical system is a transformation that takes solutions to solutions. [81%] 2021-12-24 [Dynamical Systems] [Differential Equations]...
6. Dynamical systems theory: Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. (Area of mathematics used to describe the behavior of complex dynamical systems) [81%] 2023-12-19 [Dynamical systems] [Complex systems theory]...
7. Suspension (dynamical systems): Suspension is a construction passing from a map to a flow. Namely, let X {\displaystyle X} be a metric space, f : X → X {\displaystyle f:X\to X} be a continuous map and r : X → R + {\displaystyle r:X\to ... (Dynamical systems) [81%] 2024-07-25 [Dynamical systems]
8. Combinatorics and dynamical systems: The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways. The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic ... [70%] 2023-12-13 [Combinatorics] [Dynamical systems]...
9. History of dynamical systems: Dynamical systems theory (also known as nonlinear dynamics, chaos theory) comprises methods for analyzing differential equations and iterated mappings. It is a mathematical theory that draws on analysis, geometry, and topology – areas which in turn had their origins in Newtonian ... [70%] 2021-12-24 [Dynamical Systems] [Celestial mechanics]...
10. Normal form (dynamical systems): In mathematics, the normal form of a dynamical system is a simplified form that can be useful in determining the system's behavior. Normal forms are often used for determining local bifurcations in a system. (Dynamical systems) [70%] 2023-09-29 [Bifurcation theory] [Dynamical systems]...
11. Perturbation theory (dynamical systems): The principle of perturbation theory is to study dynamical systems that are small perturbations of `simple' systems. Here simple may refer to `linear' or `integrable' or `normal form truncation', etc. (Dynamical systems) [70%] 2021-12-24 [Bifurcations] [Celestial mechanics]...
12. Piecewise smooth dynamical systems: A piecewise-smooth dynamical system (PWS) is a discrete- or continuous-time dynamical system whose phase space is partitioned in different regions, each associated to a different functional form of the system vector field. A piecewise-smooth map is described ... [70%] 2021-12-24 [Differential Equations] [Bifurcations]...
13. Dynamical systems software packages: software for dynamical systems Mathematical background on dynamical systems can be found in , or (cf. also Dynamical system). (Mathematics) [70%] 2023-10-17
14. Equivalence of dynamical systems: Two autonomous systems of ordinary differential equations (cf. Autonomous system) $$ \tag{a1 } {\dot{x} } = f ( x ) , \quad x \in \mathbf R ^ {n} , $$ and $$ \tag{a2 } {\dot{y} } = g ( y ) , \quad y \in \mathbf R ^ {n} $$ (and their associated flows, cf. (Mathematics) [70%] 2023-09-14
15. Universal behaviour in dynamical systems: In the late 1970's, P. Coullet and C. (Mathematics) [63%] 2023-10-13
16. Exponential map (discrete dynamical systems): In the theory of dynamical systems, the exponential map can be used as the evolution function of the discrete nonlinear dynamical system. The family of exponential functions is called the exponential family. (Discrete dynamical systems) [63%] 2024-02-10 [Chaotic maps]
17. Local normal forms for dynamical systems: $\def\l{\lambda}$ A local dynamical system is a dynamical system (flow of a vector field, cascade of iterates of a self-map, or sometimes more involved construction) defined in an unspecifiedly small neighborhood of a fixed (rest) point. Application ... (Mathematics) [57%] 2023-12-03