scholarly journals Role of discriminantly separable polynomials in integrable dynamical systems

2014 ◽  
Author(s):  
Vladimir Dragović ◽  
Katarina Kukić
Keyword(s):  
Dynamical Systems ◽  
Discriminantly Separable Polynomials ◽  
Integrable Dynamical Systems

scholarly journals Discriminantly separable polynomials and the generalized Kowalevski top

2017 ◽  
Vol 44 (2) ◽  
pp. 229-236 ◽  
Author(s):  
Vladimir Dragovic ◽  
Katarina Kukic
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Rigid Body ◽  
Constant Field ◽  
Explicit Integration ◽  
Heavy Rigid Body ◽  
Discriminantly Separable Polynomials ◽  
Integrable Dynamical Systems ◽  
Kowalevski Top

The notion of discriminantly separable polynomials of degree two in each of three variables has been recently introduced and related to a class of integrable dynamical systems. Explicit integration of such systems can be performed in a way similar to Kowalevski?s original integration of the Kowalevski top. Here we present the role of discriminantly separable polynomials in integration of yet another well known integrable system, the so-called generalized Kowalevski top - the motion of a heavy rigid body about a fixed point in a double constant field. We present a novel way to obtain the separation variables for this system, based on the discriminantly separable polynomials.

The Non-Causal Character of Renormalization Group Explanations

2018 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
Probability Theory ◽  
Renormalization Group ◽  
Dynamical Systems ◽  
Recent Literature ◽  
Mathematical Explanation ◽  
Causal Status ◽  
Physical Information ◽  
The Relationship ◽  
Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

Numerical characterization of nonlinear dynamical systems using parallel computing: The role of GPUs approach

2016 ◽  
Vol 37 ◽  
pp. 143-162 ◽  
Author(s):  
Filipe I. Fazanaro ◽  
Diogo C. Soriano ◽  
Ricardo Suyama ◽  
Marconi K. Madrid ◽  
José Raimundo de Oliveira ◽  
...  
Keyword(s):  
Parallel Computing ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Numerical Characterization

scholarly journals Specific and Complete Local Integration of Patterns in Bayesian Networks

2017 ◽  
Author(s):  
Martin Biehl ◽  
Takashi Ikegami ◽  
Daniel Polani
Keyword(s):  
Dynamical Systems ◽  
Lower Bound ◽  
Bayesian Networks ◽  
Upper Bound ◽  
Formal Analysis ◽  
Special Role ◽  
Local Integration

We present a first formal analysis of specific and complete local integration. Complete local integration was previously proposed as a criterion for detecting entities or wholes in distributed dynamical systems. Such entities in turn were conceived to form the basis of a theory of emergence of agents within dynamical systems. Here, we give a more thorough account of the underlying formal measures. The main contribution is the disintegration theorem which reveals a special role of completely locally integrated patterns (what we call ι-entities) within the trajectories they occur in. Apart from proving this theorem we introduce the disintegration hierarchy and its refinement-free version as a way to structure the patterns in a trajectory. Furthermore we construct the least upper bound and provide a candidate for the greatest lower bound of specific local integration. Finally, we calculate the i-entities in small example systems as a first sanity check and find that ι-entities largely fulfil simple expectations.

Sign in / Sign up

Export Citation Format

Share Document