Results 81 to 90 of about 9,394 (211)

Frequency spanning homoclinic families

, 2003
A family of maps or flows depending on a parameter $\nu$ which varies in an interval, spans a certain property if along the interval this property depends continuously on the parameter and achieves some asymptotic values along it. We consider families of
Arnold, Channon, Easton, Elskens, Gelfreich, Guckenheimer, Haberman, Henrard, Kaper, MacKay, Meiss, Meiss, Neishtadt, Neishtadt, Neı̆shtadt, Poincaré, Rom-Kedar, Rom-Kedar, Soto-Trevinõ, Tennyson, Treschev, Vered Rom-Kedar   +21 more
core   +1 more source

Pseudoholomorphic curves and multiplicity of homoclinic orbits [PDF]

Duke Mathematical Journal, 1995
The authors consider a Hamiltonian system of the form \[ \dot x = J(x) H'(t;x) \tag{1} \] on a compact, smooth Riemannian manifold \(M\). The function \(H : \mathbb{R} \times TM \to \mathbb{R}\) is smooth, 1-periodic in time and admits a point \(q_0 \in M\) such that \[ H(t; q_0, 0) = 0,\quad H'(t;q_0, 0) = 0, \] \[ H(t; q_0, p) \geq 0,\quad H(t;q,0) <
Cieliebak, Kai, Séré, Eric
openaire   +2 more sources

Closed geodesics and the first Betti number

Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.
Abstract We prove that, on any closed manifold of dimension at least two with non‐zero first Betti number, a C∞$C^\infty$ generic Riemannian metric has infinitely many closed geodesics, and indeed closed geodesics of arbitrarily large length. We derive this existence result combining a theorem of Mañé together with the following new theorem of ...
Gonzalo Contreras, Marco Mazzucchelli
wiley   +1 more source

Homoclinic orbits for a class of symmetric Hamiltonian systems

Electronic Journal of Differential Equations, 1994
of Hamiltonian systems that are symmetric with respect to independent variable (time). For the scalar case we prove existence and uniqueness of a positive homoclinic solution. For the system case we prove existence of symmetric homoclinic orbits.
Philip Korman, Alan C. Lazer
doaj  

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

Journal of Applied Mathematics, 2012
A class of first-order noncoercive discrete Hamiltonian systems are considered. Based on a generalized mountain pass theorem, some existence results of homoclinic orbits are obtained when the discrete Hamiltonian system is not periodical and need not ...
Long Yuhua
doaj   +1 more source

Homoclinic orbits for a class of $p$-Laplacian systems with periodic assumption

Electronic Journal of Qualitative Theory of Differential Equations, 2013
In this paper, by using a linking theorem, some new existence criteria of homoclinic orbits are obtained for the $p$-Laplacian system $d(|\dot{u}(t)|^{p-2}\dot{u}(t))/dt+\nabla V(t,x)=f(t)$, where $p>1$, $V(t,x)=-K(t,x)+W(t,x)$.
Xingyong Zhang
doaj   +1 more source

Protected Chaos in a Topological Lattice

Advanced Science, Volume 12, Issue 28, July 24, 2025.
Topological and chaotic dynamics are often considered incompatible, with one expected to dominate or disrupt the other. This work reveals that topological localization can persist even under strong chaotic dynamics and, counter‐intuitively, protect chaotic behavior.
Haydar Sahin, Hakan Akgün, Zhuo Bin Siu, S. M. Rafi‐Ul‐Islam, Jian Feng Kong, Mansoor B. A. Jalil, Ching Hua Lee   +6 more
wiley   +1 more source

Imperfect Homoclinic Bifurcations

, 2001
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations.
A. Arnéodo, D. V. Lyubinov, D. V. Turaev, E. Allaria, J. J. Healey, J. von Stamm, J. W. Swift, J.-M. Gambaudo, J.-M. Gambaudo, J.-M. Gambaudo, Jan Abshagen, M. Golubitsky, M. Golubitsky, M. J. B. Hauser, P. Coullet, P. Glendinning, P. Glendinning, P. Glendinning, Paul Glendinning, R. Herrero, S. M. Cox, T. Mullin, T. Peacock, Tom Mullin   +23 more
core   +1 more source

Homoclinic orbits on compact manifolds

Journal of Mathematical Analysis and Applications, 1991
Let \(M\) be a Riemannian manifold. Consider the differential equation \[ D_ t(x'(t))+\hbox{grad }V(x(t))=0,\leqno(1) \] where \(V\in C^ 2(M,{\mathbb{R}})\), \(x'\) is the derivative of the curve \(x(t)\) on \(M\), and \(D_ t(x')\) is the covariant derivative of \(x'\).
V. Benci, GIANNONI, Fabio
openaire   +3 more sources

Numerical Simulation of Mixing Enhancement in a Single Screw Extruder by Different Internal Baffles

Macromolecular Theory and Simulations, Volume 34, Issue 4, July 2025.
Three rows of plate baffles and plow‐shaped baffles are employed to introduce chaos into the flow channel of a single screw extruder. Mixing is numerically characterized in terms of the evolution of tracer particles, Poincaré sections, shear rates, mixing index, distribution probability function of mixing index, and their integral functions.
Huiwen Yu, Yuanyao Wang, Lingcao Tan, Jiarong Huang, Baiping Xu   +4 more
wiley   +1 more source