Connecting orbits for a reversible Hamiltonian system

PAUL H. RABINOWITZ

doi:10.1017/S0143385700000985

Abstract

The existence of heteroclinic and homoclinic solutions which shadow corresponding chains of such solutions is established for a class of reversible Hamiltonian systems. The proof involves elementary minimization arguments.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Bosetto, Elena Serra, Enrico and Terracini, Susanna 2002. Generic-Type Results for Chaotic Dynamics in Equations with Periodic Forcing Terms. Journal of Differential Equations, Vol. 180, Issue. 1, p. 99.

Alessio, Francesca Jeanjean, Louis and Montecchiari, Piero 2002. EXISTENCE OF INFINITELY MANY STATIONARY LAYERED SOLUTIONS INR2FOR A CLASS OF PERIODIC ALLEN–CAHN EQUATIONS. Communications in Partial Differential Equations, Vol. 27, Issue. 7-8, p. 1537.

Campos, Juan and Tarallo, Massimo 2004. Large minimal period orbits of periodic autonomous systems. Nonlinearity, Vol. 17, Issue. 1, p. 357.

Minzoni, A.A. Smyth, Noel F. and Worthy, Annette L. 2005. A variational approach to the stability of an embedded NLS soliton at the edge of the continuum. Physica D: Nonlinear Phenomena, Vol. 206, Issue. 3-4, p. 166.

Izydorek, Marek and Janczewska, Joanna 2007. Heteroclinic solutions for a class of the second order Hamiltonian systems. Journal of Differential Equations, Vol. 238, Issue. 2, p. 381.

Liu, Fei Llibre, Jaume and Zhang, Xiang 2011. Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds. Discrete & Continuous Dynamical Systems - A, Vol. 29, Issue. 3, p. 1097.

Xiang, Kaili Li, Fengying and Yu, Xiang 2015. Connecting orbits for Newtonian-like N-body problems. Journal of Inequalities and Applications, Vol. 2015, Issue. 1,

Rabinowitz, Paul H. and Montecchiari, Piero 2016. On the existence of multi-transition solutions for a class of elliptic systems. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Vol. 33, Issue. 1, p. 199.

Dipierro, Serena Patrizi, Stefania and Valdinoci, Enrico 2017. Chaotic Orbits for Systems of Nonlocal Equations. Communications in Mathematical Physics, Vol. 349, Issue. 2, p. 583.

Montecchiari, Piero and Rabinowitz, Paul H. 2018. Solutions of mountain pass type for double well potential systems. Calculus of Variations and Partial Differential Equations, Vol. 57, Issue. 5,

Rabinowitz, Paul H. and Montecchiari, Piero 2019. On global non-degeneracy conditions for chaotic behavior for a class of dynamical systems. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Vol. 36, Issue. 3, p. 627.

Dipierro, Serena Patrizi, Stefania and Valdinoci, Enrico 2019. Heteroclinic connections for nonlocal equations. Mathematical Models and Methods in Applied Sciences, Vol. 29, Issue. 14, p. 2585.

Chen, Kuo-Chang and Yu, Guowei 2020. Variational construction for heteroclinic orbits of the N-center problem. Calculus of Variations and Partial Differential Equations, Vol. 59, Issue. 1,

Yu, Guowei 2022. Heteroclinic orbits between static classes of time periodic Tonelli Lagrangian systems. Electronic Research Archive, Vol. 30, Issue. 6, p. 2283.

Article contents

Connecting orbits for a reversible Hamiltonian system

Abstract

Access options

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Connecting orbits for a reversible Hamiltonian system

Abstract

Access options

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests