Results 11 to 20 of about 101,401 (197)
Журнал Средневолжского математического общества, 2022 This paper introduces class $G$ containing Cartesian products of orientation-changing rough transformations of the circle and studies their dynamics. As it is known from the paper of A. G. Maier non-wandering set of orientation-changing diffeomorphism of
Zinina Svetlana Kh., Pochinka Pavel I.
doaj +1 more source
Dimension and product structure of hyperbolic measures [PDF]
, 1999 We prove that every hyperbolic measure invariant under a C^{1+\alpha} diffeomorphism of a smooth Riemannian manifold possesses asymptotically ``almost'' local product structure, i.e., its density can be approximated by the product of the densities on ...
Barreira, Luis +2 more
core +7 more sources
Slow invariant manifolds as curvature of the flow of dynamical systems [PDF]
, 2014 Considering trajectory curves, integral of n-dimensional dynamical systems, within the framework of Differential Geometry as curves in Euclidean n-space, it will be established in this article that the curvature of the flow, i.e.
Chua, Leon +2 more
core +1 more source
Nondense orbits for Anosov diffeomorphisms of the $2$-torus [PDF]
, 2016 Let $\lambda$ denote the probability Lebesgue measure on ${\mathbb T}^2$. For any $C^2$-Anosov diffeomorphism of the $2$-torus preserving $\lambda$ with measure-theoretic entropy equal to topological entropy, we show that the set of points with nondense ...
Tseng, Jimmy
core +3 more sources
The Universe from Scratch [PDF]
, 2005 A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19th-century founders of modern geometry contemplated the possibility that a piece of empty space that ...
Ambjorn, J., Jurkiewicz, J., Loll, R.
core +9 more sources
Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems [PDF]
, 2015 We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a hybrid dynamical ...
Burden, Samuel A. +2 more
core +1 more source
Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion [PDF]
, 2015 In this tutorial, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to demonstrate the ...
Kuznetsov, N. V. +2 more
core +1 more source
Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics [PDF]
, 2017 We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics.
Banisch, Ralf +5 more
core +2 more sources
Dimension estimation for autonomous nonlinear systems [PDF]
, 2015 The problem of estimating the dimension of the state-space of an autonomous nonlinear system is considered. Assuming that sampled measurements of the output and finitely many of its time derivatives are available, an exhaustive search algorithm able to ...
Astolfi, A, Padoan, A
core +1 more source
Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems
, 2010 Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a surface on ...
Arima +85 more
core +1 more source