His main field of research is the theory of dynamical systems.His contributions are multifaceted and have shaped large areas within dynamical systems in many ways, and he is known for his unusually comprehensive view of the field and his understanding of the interaction of its parts as well as its connections to other fields.…

Shape Dynamics possesses a physical arrow of time given by the growth of complexity and the dynamical storage of locally accessible records of the past.This is a property of the dynamical law and does not require any special initial condition.…

The steady-state values are also very slightly dependent on the strain-rate.Many systems in nature reach steady-states and dynamical systems theory is used to describe such systems.Soil shear can also be described as a dynamical system.…

In such cases, dynamical systems theory may be used for analysis.

His main scientific interest during these years was in ergodic theory and dynamical systems.

Dynamical systems are defined over a single independent variable, usually thought of as time.A more general class of systems are defined over multiple independent variables and are therefore called multidimensional systems.…

In 1993, she constructed a smooth counterexample to the Seifert conjecture.She has since continued to work in dynamical systems.…

Amongst the algorithms she had studied, are the celebrated LLL algorithm used for basis reductions in Euclidean lattice and the different Euclidean algorithms to determine GCD.The main tool used to achieve her results is the so-called dynamical analysis.Loosely speaking, it is a mix between analysis of algorithms and dynamical systems.…

The first of these groups of properties may be called dynamical; the others, chemical.The dynamic value of water when it falls upon the land is the amount of energy it can apply in going down the slope which separates it from the sea.…Cited from Outlines of the Earth's History, by Nathaniel Southgate Shaler

The contraforte has a written range from A1 - G5 (in scientific pitch notation), which sounds as A0 - G4.Large toneholes allow for a free response and a very large dynamical range.The pivot screws lie in synthetic sleeves for silent key actions, and push rods make for easy key action with low friction.…

In mathematics, especially in the study of dynamical systems, a limit set is the state a dynamical system reaches after an infinite amount of time has passed, by either going forward or backwards in time.Limit sets are important because they can be used to understand the long term behavior of a dynamical system.…

Many real dynamical systems do not exactly fit this model.In fact, unmodelled dynamics can seriously degrade the filter performance, even when it was supposed to work with unknown stochastic signals as inputs.…

Students of vector fields and Lie theory often encounter the Jacobi identity, the analog of associativity for the Lie bracket operation.Planetary theory and other particular dynamical problems likewise occupied his attention from time to time.While contributing to celestial mechanics, he introduced the Jacobi integral (1836) for a sidereal coordinate system.…

The agent's artificial brain comprises two major components: a learning system and a decision-making system.The learning system models the agent's environment as a dynamical system.…

Reaction-diffusion systems are naturally applied in chemistry.However, the system can also describe dynamical processes of non-chemical nature.Examples are found in biology, geology and physics and ecology.…

He was one of the leading experts on the theory of dynamical systems.

At the same time he was considering questions unrelated to stochastic processes.For example, he constructed an example of a dynamical system with a simple spectrum.In collaboration with B. S. Mityagin he worked on quasi-invariant measures on topological linear spaces.…

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 combinatorics.Also dynamical systems theory is heavily involved in the relatively recent field of combinatorics on words.Also combinatorial aspects of dynamical systems are studied.…

Eggen's argument that groups of this type are in fact cluster remnants has been debated.It has been noted that because such phenomena may also be the result of other dynamical mechanisms.…

These engines allow simulation of the way bodies of many types are affected by a variety of physical stimuli.They are also used to create Dynamical simulations without having to know anything about physics.Physics engines are used throughout the video game and movie industry, but not all physics engines are alike; They are generally broken into real-time and the high precision but these are not the only options.…