Results 1 to 10 of about 7,257 (197)
Homoclinic Orbits for a Class of Nonperiodic Hamiltonian Systems with Some Twisted Conditions [PDF]
Abstract and Applied Analysis, 2013 By the Maslov index theory, we will study the existence and multiplicity of homoclinic orbits for a class of asymptotically linear nonperiodic Hamiltonian systems with some twisted conditions on the Hamiltonian functions.
Qi Wang, Qingye Zhang
doaj +2 more sources
Collision, explosion and collapse of homoclinic classes [PDF]
Nonlinearity, 2004 Homoclinic classes of generic $C^1$-diffeomorphisms are maximal transitive sets and pairwise disjoint. We here present a model explaining how two different homoclinic classes may intersect, failing to be disjoint. For that we construct a one-parameter family of diffeomorphisms $(g_s)_{s\in [-1,1]}$ with hyperbolic points $P$ and $Q$ having nontrivial ...
Lorenzo J. Díaz, Bianca Santoro
openalex +4 more sources
Homoclinic classes for sectional-hyperbolic sets [PDF]
Kyoto Journal of Mathematics, 2016 We prove that every sectional-hyperbolic Lyapunov stable set contains a nontrivial homoclinic class.
Alexander Arbieto +2 more
openalex +5 more sources
Continuum-wise expansive homoclinic classes for robust dynamical systems [PDF]
Advances in Difference Equations, 2019 In the study, we consider continuum-wise expansiveness for the homoclinic class of a kind of C1 $C^{1}$-robustly expansive dynamical system. First, we show that if the homoclinic class H(p,f) $H(p, f)$, which contains a hyperbolic periodic point p, is R ...
Manseob Lee
doaj +2 more sources
Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations [PDF]
Journal of Applied Mathematics, 2012 The authors study the existence and uniqueness of a set with 2kT-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a ...
Lijuan Chen, Shiping Lu
doaj +2 more sources
Structurally Stable Homoclinic Classes [PDF]
, 2014 In this paper we study structurally stable homoclinic classes. In a natural way, the structural stability for an individual homoclinic class is defined through the continuation of periodic points.
Wen, Xiao
core +3 more sources
Homoclinic Solutions for a Class of Nonlinear Difference Equations [PDF]
Journal of Applied Mathematics, 2014 We prove the existence of homoclinic solutions of a class of nonlinear difference equations with superlinear nonlinearity by using the generalized Nehari manifold approach.
Ali Mai, Zhan Zhou
doaj +3 more sources
Periodic points and homoclinic classes [PDF]
Ergodic Theory and Dynamical Systems, 2006 We prove that there is a residual subset $\mathcal{I}$ of ${\rm Diff}^1({\it M})$ such that any homoclinic class of a diffeomorphism $f\in \mathcal{I}$ having saddles of indices $\alpha$ and $\beta$ contains a dense subset of saddles of index $\tau$ for every $\tau\in [\alpha,\beta]\cap \mathbb{N}$.
Flavio Abdenur +4 more
openalex +5 more sources
Homoclinic Solutions for a Class of the Second-Order Impulsive Hamiltonian Systems [PDF]
Abstract and Applied Analysis, 2013 This paper is concerned with the existence of homoclinic solutions for a class of the second order impulsive Hamiltonian systems. By employing the Mountain Pass Theorem, we demonstrate that the limit of a 2kT-periodic approximation solution is a ...
Jingli Xie, Zhiguo Luo, Guoping Chen
doaj +2 more sources
New homoclinic solutions for a class of second-order Hamiltonian systems with a mixed condition [PDF]
Boundary Value Problems, 2018 In this paper, we introduce a new mixed condition to obtain a new compact embedding theorem. Under this theorem, we study the existence and multiplicity of nontrivial homoclinic solutions for a class of second-order Hamiltonian systems with variable ...
Xuefeng Li, Jin Jia
doaj +2 more sources