Stochasticity in dynamical systems and the curvature of the associated riemannian manifold

1985 ◽  
Vol 109 (2) ◽  
pp. 395-397
Author(s):  
H. Varvoglis
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems

Dynamical systems: Approximate Lagrangians and Noether symmetries

2019 ◽  
Vol 16 (10) ◽  
pp. 1950160 ◽  
Author(s):  
Sameerah Jamal
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems ◽  
Variational Principle ◽  
Kinetic Energy ◽  
Equations Of Motion ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Geometric Conditions ◽  
Finite Dimensional ◽  
Second Order Equations

We determine the approximate Noether point symmetries of the variational principle characterizing second-order equations of motion of a particle in a (finite-dimensional) Riemannian manifold. In particular, the Lagrangian comprises of kinetic energy and a potential [Formula: see text], perturbed to [Formula: see text]. We establish a convenient system of approximate geometric conditions that suffices for the computation of approximate Noether symmetry vectors and moreover, simplifies the problem of the effect of higher orders of the perturbation. The general results are applied to several practical problems of interest and we find extra Noether symmetries at [Formula: see text].

Dynamical systems on a Riemannian manifold that admit normal shift

1995 ◽  
Vol 103 (2) ◽  
pp. 543-549
Author(s):  
A. Yu. Boldin ◽  
V. V. Dmitrieva ◽  
S. S. Safin ◽  
R. A. Sharipov
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems ◽  
Normal Shift

scholarly journals Isometries and certain dynamical systems

1984 ◽  
Vol 30 (2) ◽  
pp. 239-246 ◽  
Author(s):  
Saber Elaydi ◽  
Hani R. Farran
Keyword(s):  
Dynamical System ◽  
Riemannian Manifold ◽  
Dynamical Systems

It is shown that there exists a metric under which a diffeomorphism f on a Riemannian manifold M becomes an isometry, provided that the dynamical system generated by f is of characteristic 0± and all its orbits are closed. Furthermore, it is shown that the foliation given by the suspension of f is parallel in this case.

Pseudo-Riemannian manifold of mixmaster dynamical systems

1990 ◽  
Vol 148 (5) ◽  
pp. 239-245 ◽  
Author(s):  
M. Szydłowski ◽  
A. Ł;apeta
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems

Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties

1992 ◽  
Vol 12 (1) ◽  
pp. 123-151 ◽  
Author(s):  
Ya. B. Pesin
Keyword(s):  
Riemannian Manifold ◽  
Dynamical Systems ◽  
Invariant Measure ◽  
Topological Properties ◽  
Smooth Measure ◽  
Ergodic Properties ◽  
Special Invariant ◽  
Hyperbolic Attractors ◽  
Hyperbolic Behavior

AbstractWe introduce a class of dynamical systems on a Riemannian manifold with singularities having attractors with strong hyperbolic behavior of trajectories. This class includes a number of famous examples such as the Lorenz type attractor, the Lozi attractor and some others which have been of great interest in recent years. We prove the existence of a special invariant measure which is an analog of the Bowen-Ruelle-Sinai measure for classical hyperbolic attractors and study the ergodic properties of the system with respect to this measure. We also describe some topological properties of the system on the attractor. Our results can be considered a dissipative version of the theory of systems with singularities preserving the smooth measure.

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