Results 61 to 70 of about 2,789,352 (166)
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
Newhouse phenomenon and homoclinic classes
, 2010 We show that for a C1 generic subset of diffeomorphisms far from homoclinic tangencies, any infinite sequence of sinks or sources must accumulate on a homoclinic class of some saddle point with codimension one.
JIAGANG YANG
core +1 more source
Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems
Abstract and Applied Analysis, 2012 We study the following nonperiodic Hamiltonian system ż=JHz(t,z), where H∈C1(R×R2N,R) is the form H(t,z)=(1/2)B(t)z⋅z+R(t,z). We introduce a new assumption on B(t) and prove that the corresponding Hamiltonian operator has only point spectrum.
Wenping Qin, Jian Zhang, Fukun Zhao
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 +6 more
wiley +1 more source
Center Manifolds for Homoclinic Solutions
, 2000 In this article, center-manifold theory is developed for homoclinic solutions of ordinary differential equations or semilinear parabolic equations. A center manifold along a homoclinic solution is a locally invariant manifold containing all solutions ...
Sandstede, Björn
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Abstract and Applied Analysis, 2012 A class of difference equations which include discrete nonlinear Schrödinger equations as special cases are considered. New sufficient conditions of the existence and multiplicity results of homoclinic solutions for the difference equations are obtained ...
Defang Ma, Zhan Zhou
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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 +4 more
wiley +1 more source
, 2018 For a class of three-dimensional piecewise affine systems, this paper focuses on the existence of homoclinic cycles and the phenomena of homoclinic bifurcation leading to periodic orbits.
Xiao-Song Yang, Lei Wang
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Homoclinic orbits at infinity for second-order Hamiltonian systems with fixed energy
Electronic Journal of Differential Equations, 2015 We obtain the existence of homoclinic orbits at infinity for a class of second-order Hamiltonian systems with fixed energy. We use the limit for a sequence of approximate solutions which are obtained by variational methods.
Dong-Lun Wu, Shiqing Zhang
doaj
Harmonic Balance for Non-Periodic Hyperbolic Solutions of Nonlinear Ordinary Differential Equations
Mathematical Modelling and Analysis, 2017 In this paper, we propose a new approach for obtaining explicit analytical approximations to the homoclinic or heteroclinic solutions of a general class of strongly nonlinear ordinary differential equations describing conservative singledegree-of-freedom
Serge Bruno Yamgoue +2 more
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