Cover Image

Connections to fixed points and Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems

We consider a singularly perturbed system depending on two parameters with two (possibly the same) normally hyperbolic center manifolds. We assume that the unperturbed system has an orbit that connects a hyperbolic fixed point on one center manifold to a hyperbolic fixed point on the other. Then we...

Full description

Saved in:

Bibliographic Details
Date:	2008
Main Authors:	Battelli, F., Palmer, K. J., Баттеллі, Ф., Палмер, К. Дж.
Format:	Article
Language:	English
Published:	Institute of Mathematics, NAS of Ukraine 2008
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/3135
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

Connections to fixed points and Sil’nikov saddle-focus homoclinic orbits in singularly perturbed systems
by: Battelli, F., et al.
Published: (2008)

Bifurcation structure of interval maps with orbits homoclinic to a saddle-focus
by: C. Hinsley, et al.
Published: (2023)

Bifurcation structure of interval maps with orbits homoclinic to a saddle-focus
by: Hinsley, Carter, et al.
Published: (2024)

Heteroclinic Orbits and Nonintegrability in Two-Degree-of-Freedom Hamiltonian Systems with Saddle-Centers
by: Yagasaki, K., et al.
Published: (2019)

Homoclinic Points for a Singularly Perturbed System of Differential Equations with Delay
by: Klevchuk, I. I., et al.
Published: (2002)

The Lyapunov–Schmidt Approach to Studying Homoclinic Splitting in Weakly Perturbed Lagrangian and Hamiltonian Systems
by: Samoilenko, A.M., et al.
Published: (2003)

Lyapunov–Schmidt Approach to Studying Homoclinic Splitting in Weakly Perturbed Lagrangian and Hamiltonian Systems
by: Prykarpatsky, A. K., et al.
Published: (2003)

Mel’nikov-Samoilenko adiabatic stability problem
by: Prykarpatsky, Ya. A., et al.
Published: (2006)

The Poincare-Mel'nikov geometric analysis of the transversal splitting of manifolds of slowly perturbed nonlinear dynamical systems. I
by: Prykarpatsky, A. K., et al.
Published: (1993)

The Clay Model of the Saddle from Tsyrkuny Hill-fort
by: Ju. Peljashenko
Published: (2016)

Simplex analysis of dynamical systems with a perturbation. New criteria of stabilization of a homoclinic separatrix and its use
by: Mitropolsky , Yu. O., et al.
Published: (1992)

Spurs from the Sanctuary at Gurzuf Saddle Pass in the Crimean Mountains
by: M. V. Novychenkova
Published: (2013)

Navier Stokes Equation and Homoclinic Chaos
by: Покутний, Олександр Олексійович
Published: (2019)

Navier Stokes Equation and Homoclinic Chaos
by: O. O. Pokutnyi
Published: (2019)

Perturbed (2 − 1)-Dimensional Kepler Problem and the Nilpotent Adjoint Orbits of (, )
by: Odzijewicz, Anatol
Published: (2020)

The order of coexistence of homoclinic trajectories for interval maps
by: M. V. Kuznietsov
Published: (2019)

The order of coexistence of homoclinic trajectories for interval maps
by: Kuznietsov, M. V., et al.
Published: (2019)

The Model of Saddle from Tsyrkuny Hill-fort (comment on the article of K. Pelyashenko)
by: A. V. Simonenko
Published: (2016)

Saddle point excitonic resonances in BiI3 layered single crystals
by: Kudryavtsev, O.O., et al.
Published: (1999)

Kotel'nikov-Shannon formula for Fourier transforms of distributions with compact supports
by: Izvekov, I. G., et al.
Published: (1995)

Bounded solutions of the nonlinear Lyapunov equation and homoclinic chaos
by: O. A. Boichuk, et al.
Published: (2019)

Bounded solutions of the nonlinear Lyapunov equation and homoclinic chaos
by: Boichuk, О. A., et al.
Published: (2019)

Paleogeography features of Tournasian-Visean time of the area of Mechedivsko-Sviridivska saddle and adjacent territories
by: P. M. Korzhnev, et al.
Published: (2018)

Multidimensional Lagrange–Yen-Type Interpolation Via Kotel'nikov–Shannon Sampling Formulas
by: Pogány, T.K.
Published: (2003)

Multidimensional Lagrange–Yen-Type Interpolation Via Kotel'nikov–Shannon Sampling Formulas
by: Pogány, T. K., et al.
Published: (2003)

On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point
by: Chuchman, Ivan
Published: (2018)

On a semigroup of closed connected partial homeomorphisms of the unit interval with a fixed point
by: Chuchman, I.
Published: (2011)

Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum
by: Pashitskii, E.A., et al.
Published: (1999)

About the existence of a homoclinic trajectory with symmetry in the three-dimensional systems
by: N. V. Nikitina
Published: (2014)

Orbit Functions
by: Klimyk, A., et al.
Published: (2006)

Infinitely many fast homoclinic solutions for some second-order nonautonomous systems
by: Yang, Liu, et al.
Published: (2014)

Infinitely Many Fast Homoclinic Solutions for Some Second-Order Nonautonomous Systems
by: Luo, Liping, et al.
Published: (2014)

Antisymmetric Orbit Functions
by: Klimyk, A., et al.
Published: (2007)

E-Orbit Functions
by: Klimyk, A.U., et al.
Published: (2008)

Hamiltonian geometric connection associated with adiabatically perturbed Hamiltonian systems and the existence of adiabatic invariants
by: Prykarpatsky, Ya. A., et al.
Published: (2008)

Focusing by wakefield and plasma focusing of relativistic electrons in dependence on parameters of experiments
by: Levchuk, I.P., et al.
Published: (2016)

Launch Vehicle Rendezvous to Catalogued Orbital Debris while Injecting into Highly-Inclined Orbits
by: O. V. Holubek, et al.
Published: (2020)

Multiple fast homoclinic solutions for a class of second-order differential systems with p-Laplacian
by: W. Selmi
Published: (2024)

Two different sequences of infinitely many homoclinic solutions for a class of fractional Hamiltonian systems
by: A. Benhassine
Published: (2023)

Two different sequences of infinitely many homoclinic solutions for a class of fractional Hamiltonian systems
by: Benhassine, A., et al.
Published: (2023)