Conservation laws and thermodynamic formalism for Dissipative Dynamical Systems

1989 ◽  
Vol 12 (3) ◽  
pp. 1-72 ◽  
Author(s):  
R. Badii
Keyword(s):  
Dynamical Systems ◽  
Conservation Laws ◽  
Thermodynamic Formalism ◽  
Dissipative Dynamical Systems

On the Characterization of the Scaling Behavior of Dissipative Dynamical Systems through a Generalized Entropy

1991 ◽  
Vol 46 (7) ◽  
pp. 642-644 ◽  
Author(s):  
R. Stoop ◽  
J. Parisi ◽  
H. Brauchli
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Thermodynamic Formalism ◽  
Relevant Information ◽  
Numerical Approach ◽  
Scaling Behavior ◽  
Model Systems ◽  
Generalized Entropy ◽  
Dissipative Dynamical Systems

Different aspects of the scaling behavior of a dissipative dynamical system arc obtained in a straightforward way from the associated generalized entropy function which, in this way, embodies the relevant information on the scaling behavior of the system. This is demonstrated by the application of the thermodynamic formalism to two model systems for each of which, however, a specific numerical approach must be followed in order to overcome the numerical problems.

Shape of attractors for three-dimensional dissipative dynamical systems

2000 ◽  
Vol 61 (5) ◽  
pp. 5098-5107 ◽  
Author(s):  
S. Neukirch ◽  
H. Giacomini
Keyword(s):  
Dynamical Systems ◽  
Three Dimensional ◽  
Dissipative Dynamical Systems

scholarly journals Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

2004 ◽  
Vol 297 (1) ◽  
pp. 152-168 ◽  
Author(s):  
Nail H Ibragimov ◽  
Gazanfer Ünal ◽  
Claes Jogréus
Keyword(s):  
Dynamical Systems ◽  
Conservation Laws ◽  
Approximate Symmetries

Lagrangian Mechanics

2019 ◽  
pp. 53-82
Author(s):  
David D. Nolte
Keyword(s):  
Dynamical Systems ◽  
Conservation Laws ◽  
Euler Equations ◽  
Virial Theorem ◽  
Variational Calculus ◽  
Mechanical Action ◽  
Lagrange Equations ◽  
Time Average ◽  
The Difference ◽  
Kinetic And Potential Energies

Dynamical systems follow trajectories for which the mechanical action integrated along the trajectory is an extremum. The action is defined as the time average of the difference between kinetic and potential energies, which is also the time average of the Lagrangian. Once a Lagrangian has been defined for a system, the Euler equations of variational calculus lead to the Euler–Lagrange equations of dynamics. This chapter explores applications of Lagrangians and the use of Lagrange’s undetermined multipliers. Conservation laws, central forces, and the virial theorem are developed and explained.

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