Now showing items 1-19 of 19

• #### A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies ﻿

(2014-07)
Research report
Open Access
• #### Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio ﻿

(2014-09)
Research report
Open Access
We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider ...
• #### Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio ﻿

(Springer, 2014-11)
Article
Open Access
We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We ...
• #### Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies ﻿

(2013)
Research report
Open Access
We study the splitting of invariant manifolds of whiskered t ori with two or three frequencies in nearly-integrable Hamiltonian systems. We consider 2-dimensional tori with a frequency vector ω = (1 , Ω) where Ω is ...
• #### Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tort with quadratic and cubic frequencies ﻿

(2014-01-01)
Article
Open Access
We study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus ...
• #### Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type ﻿

(2014-02)
Research report
Open Access
We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with ...
• #### Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio ﻿

(2016-06)
Article
Open Access
The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. We consider a torus with a fast ...
• #### Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio ﻿

(2015)
Research report
Open Access
The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied.
• #### Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies ﻿

(2020-01-01)
Article
Open Access
We study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional torus ...
• #### Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies ﻿

(2019-06)
Research report
Open Access
We study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional ...
• #### Homoclinic phenomena in conservative systems ﻿

(Universitat Politècnica de Catalunya, 2013-04-29)
Doctoral thesis
Open Access
The goal of this thesis is the study of homoclinic orbits in conservative systems (area-preserving maps and Hamiltonian systems). We consider homoclinic (bi-asymptotic) orbits either to saddle periodic orbits or to whiskered ...
• #### Mixed dynamics of two-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies ﻿

(American Institute of Mathematical Sciences, 2018-09)
Article
Open Access
We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We ...
• #### On bifurcations of area-preserving and nonorientable maps with quadratic homoclinic tangencies ﻿

(Springer, 2014)
Article
Open Access
We study bifurcations of nonorientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on nonorientable two-dimensional surfaces. We consider one- and two-parameter ...
• #### On bifurcations of homoclinic tangencies in area-preserving maps on non-orientable manifolds ﻿

(Springer, 2016)
Part of book or chapter of book
Restricted access - publisher's policy
We study bifurcations of non-orientable area-preserving maps with quadratic homoclinic tangencies. We study the case when the maps are given on non-orientable two-dimensional manifolds. We consider one and two parameter ...
• #### On dynamics and bifurcations of area-preserving maps with homoclinic tangencies ﻿

(2015-09-01)
Article
Open Access
We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to ...
• #### On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps ﻿

(Institute of Physics (IOP), 2018-04-30)
Article
Open Access
We study the 1:4 resonance for the conservative cubic Hénon maps C^± with positive and negative cubic terms. These maps show up different bifurcation structures both for fixed points with eigenvalues¿±i and for 4-periodic ...
• #### Reversible perturbations of conservative Hénon-like maps ﻿

(2021-04-01)
Article
Open Access
For area-preserving Hénon-like maps and their compositions, we consider smooth perturbations that keep the reversibility of the initial maps but destroy their conservativity. For constructing such perturbations, we use two ...
• #### The dynamics of digits: calculating Pi with Galperin's billiards ﻿

(Multidisciplinary Digital Publishing Institute (MDPI), 2020-04-01)
Article
Open Access
In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number p . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of p ...
• #### Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves ﻿

(2021-01-01)
Article
Open Access
The recently proposed map [arXiv:2011.01415] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [Phys. Rev. X 9, 021035 (2019)] and the high-density zero-temperature triangular ...