Higher order first integrals of autonomous dynamical systems

2021 ◽  
Vol 170 ◽  
pp. 104383
Author(s):  
Antonios Mitsopoulos ◽  
Michael Tsamparlis
Keyword(s):  
Dynamical Systems ◽  
Higher Order ◽  
First Integrals ◽  
Autonomous Dynamical Systems

scholarly journals Unified formalism for higher order non-autonomous dynamical systems

2012 ◽  
Vol 53 (3) ◽  
pp. 032901 ◽  
Author(s):  
Pedro Daniel Prieto-Martínez ◽  
Narciso Román-Roy
Keyword(s):  
Dynamical Systems ◽  
Higher Order ◽  
Autonomous Dynamical Systems

scholarly journals Unified formalism for the generalized kth-order Hamilton–Jacobi problem

2014 ◽  
Vol 11 (09) ◽  
pp. 1460037 ◽  
Author(s):  
Leonardo Colombo ◽  
Manuel De Léon ◽  
Pedro Daniel Prieto-Martínez ◽  
Narciso Román-Roy
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hamiltonian Formalism ◽  
Higher Order ◽  
Lagrangian Functions ◽  
Geometric Formulation ◽  
Autonomous Dynamical Systems

The geometric formulation of the Hamilton–Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian–Hamiltonian formalism for the geometric Hamilton–Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.

HIGHER ORDER CELLULAR AUTOMATA

2005 ◽  
Vol 08 (02n03) ◽  
pp. 169-192 ◽  
Author(s):  
NILS A. BAAS ◽  
TORBJØRN HELVIK
Keyword(s):  
Dynamical Systems ◽  
Cellular Automata ◽  
Level Structure ◽  
Higher Order ◽  
New Concepts ◽  
Multi Level

We introduce a class of dynamical systems called Higher Order Cellular Automata (HOCA). These are based on ordinary CA, but have a hierarchical, or multi-level, structure and/or dynamics. We present a detailed formalism for HOCA and illustrate the concepts through four examples. Throughout the article we emphasize the principles and ideas behind the construction of HOCA, such that these easily can be applied to other types of dynamical systems. The article also presents new concepts and ideas for describing and studying hierarchial dynamics in general.

scholarly journals State space decomposition for non-autonomous dynamical systems

2011 ◽  
Vol 141 (5) ◽  
pp. 957-974 ◽  
Author(s):  
Xiaopeng Chen ◽  
Jinqiao Duan
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
State Space ◽  
Decomposition Theorem ◽  
Navier Stokes ◽  
Locally Compact ◽  
Infinite Dimensional ◽  
The Lorenz System ◽  
A Chain ◽  
Autonomous Dynamical Systems

The decomposition of state spaces into dynamically different components is helpful for understanding dynamics of complex systems. A Conley-type decomposition theorem is proved for non-autonomous dynamical systems defined on a non-compact but separable state space. Specifically, the state space can be decomposed into a chain-recurrent part and a gradient-like part. This result applies to both non-autonomous ordinary differential equations on a Euclidean space (which is only locally compact), and to non-autonomous partial differential equations on an infinite-dimensional function space (which is not even locally compact). This decomposition result is demonstrated by discussing a few concrete examples, such as the Lorenz system and the Navier–Stokes system, under time-dependent forcing.

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