Results 41 to 50 of about 57,997 (153)

Fractional Generalization of Gradient and Hamiltonian Systems

, 2005
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space.
Tarasov, Vasily E.
core   +2 more sources

A Coordinate-Free Variational Approach to Fourth-Order Dynamical Systems on Manifolds: A System and Control Theoretic Viewpoint

Mathematics
The present paper describes, in a theoretical fashion, a variational approach to formulate fourth-order dynamical systems on differentiable manifolds on the basis of the Hamilton–d’Alembert principle of analytic mechanics.
Simone Fiori
doaj   +1 more source

Dynamical Systems Method (DSM) for solving nonlinear operator equations in Banach spaces [PDF]

, 2010
Let $F(u)=h$ be an operator equation in a Banach space $X$, $\|F'(u)-F'(v)\|\leq \omega(\|u-v\|)$, where $\omega\in C([0,\infty))$, $\omega(0)=0$, $\omega(r)>0$ if $r>0$, $\omega(r)$ is strictly growing on $[0,\infty)$. Denote $A(u):=F'(u)$, where $F'(u)$
Ramm, A. G.
core   +7 more sources

Ergodic theory of generic continuous maps

, 2012
We study the ergodic properties of generic continuous dynamical systems on compact manifolds. As a main result we prove that generic homeomorphisms have convergent Birkhoff averages under continuous observables at Lebesgue almost every point. In spite of
Abdenur, Flávio, Andersson, Martin
core   +1 more source

Bounds of Different Integral Operators in Tensorial Hilbert and Variable Exponent Function Spaces

Mathematics
In dynamical systems, Hilbert spaces provide a useful framework for analyzing and solving problems because they are able to handle infinitely dimensional spaces.
Waqar Afzal, Mujahid Abbas, Omar Mutab Alsalami   +2 more
doaj   +1 more source

On the policy function in continuos time economic models [PDF]

, 1991
In this paper, I consider a general class of continuous-time economic models with unbounded horizon. I study the sets of conditions under which the policy function is continuous, Lipschitz continuous, and Cl differentiable.
Santos, Manuel S.
core   +1 more source

Hierarchical decomposition of LTL synthesis problem for nonlinear control systems

, 2019
This paper deals with the control synthesis problem for a continuous nonlinear dynamical system under a Linear Temporal Logic (LTL) formula. The proposed solution is a top-down hierarchical decomposition of the control problem involving three abstraction
Dimarogonas, Dimos V., Meyer, Pierre-Jean   +1 more
core   +2 more sources

A Garden of Eden theorem for Anosov diffeomorphisms on tori

, 2016
Let $f$ be an Anosov diffeomorphism of the $n$-dimensional torus ${\mathbb{T}}^n$ and $\tau$ a continuous self-mapping of ${\mathbb{T}}^n$ commuting with $f$.
Ceccherini-Silberstein, Tullio, Coornaert, Michel   +1 more
core   +1 more source

Multi-exit Kolmogorov–Arnold networks: enhancing accuracy and parsimony

Machine Learning: Science and Technology
Kolmogorov–Arnold networks (KANs) uniquely combine high accuracy with interpretability, making them valuable for scientific modeling. However, it is unclear a priori how deep a network needs to be for any given task, and deeper KANs can be difficult to ...
James Bagrow, Josh Bongard
doaj   +1 more source

Discrete Dynamical Systems Embedded in Cantor Sets

, 2006
While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $ N $ variables, as binary neural networks and cellular automata.
Alberto Verjovsky, Atkinson K. E., Choquet-Bruhat Y., Devaney R., Fabio Benatti, Federico Zertuche, Hertz J., Kauffman S. A., Pontrjagin L., Weisbuch G., Wiggins S., Wolfram S.   +11 more
core   +3 more sources