Results 61 to 70 of about 7,276 (215)

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

Discrete Schrödinger equations in the nonperiodic and superlinear cases: homoclinic solutions

Advances in Difference Equations, 2017
Using variational methods, we study the existence and multiplicity of homoclinic solutions for a class of discrete Schrödinger equations in infinite m-dimensional lattices with nonlinearities being superlinear at infinity.
Liqian Jia, Jun Chen, Guanwei Chen
doaj   +1 more source

Measure-Expansive Homoclinic Classes for C¹ Generic Flows

Mathematics, 2020
In this paper, we prove that for a generically C1 vector field X of a compact smooth manifold M, if a homoclinic class H(γ,X) which contains a hyperbolic closed orbit γ is measure expansive for X then H(γ,X) is hyperbolic.
Manseob Lee
doaj   +1 more source

Infinitely many homoclinic solutions for a class of damped vibration problems

Electronic Journal of Qualitative Theory of Differential Equations, 2022
In this paper, we consider the multiplicity of homoclinic solutions for the following damped vibration problems $$ \ddot{x}(t)+B\dot{x}(t)-A(t)x(t)+H_{x}(t,x(t))=0,$$ where $A(t)\in (\mathbb{R},\mathbb{R}^{N})$ is a symmetric matrix for all $t\in \mathbb{
Huijuan Xu, Shan Jiang, Guanggang Liu
doaj   +1 more source

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

Computational complexity, torsion-freeness of homoclinic Floer homology, and homoclinic Morse inequalities

, 2017
Floer theory was originally devised to estimate the number of 1-periodic orbits of Hamiltonian systems. In earlier works, we constructed Floer homology for homoclinic orbits on two dimensional manifolds using combinatorial techniques.
Hohloch, Sonja
core   +1 more source

Periodic measures and partially hyperbolic homoclinic classes

Transactions of the American Mathematical Society, 2019
In this paper, we give a precise meaning to the following fact, and we prove it: $C^1$-open and densely, all the non-hyperbolic ergodic measures generated by a robust cycle are approximated by periodic measures. We apply our technique to the global setting of partially hyperbolic diffeomorphisms with one dimensional center. When both strong stable and
Bonatti, Christian, Zhang, Jinhua
openaire   +4 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

Ground-state sign-changing homoclinic solutions for a discrete nonlinear p-Laplacian equation with logarithmic nonlinearity

Boundary Value Problems
By using a direct non-Nehari manifold method from (Tang and Cheng in J. Differ. Equ. 261:2384–2402, 2016), we obtain an existence result of ground-state sign-changing homoclinic solutions that only changes sign once and ground-state homoclinic solutions ...
Xin Ou, Xingyong Zhang
doaj   +1 more source

Existence and Orbital Stability of Standing‐Wave Solutions of the Nonlinear Logarithmic Schrödinger Equation On a Tadpole Graph

Studies in Applied Mathematics, Volume 155, Issue 1, July 2025.
ABSTRACT This work aims to study some dynamical aspects of the nonlinear logarithmic Schrödinger equation (NLS‐log) on a tadpole graph, namely, a graph consisting of a circle with a half‐line attached at a single vertex. By considering Neumann–Kirchhoff boundary conditions at the junction, we show the existence and the orbital stability of standing ...
Jaime Angulo Pava, Andrés Gerardo Pérez Yépez   +1 more
wiley   +1 more source