Contracting Lorenz Attractors through Resonant Double Homoclinic Loops

DOI10.1137/S0036141004443907zbMath1107.37041OpenAlexW4241197571MaRDI QIDQ5470646

Maria Jose Pacifico, Bernardo San Martín Rebolledo, Carlos A. Morales

Publication date: 31 May 2006

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036141004443907

zbMATH Keywords

three-dimensional vector fieldresonant double homoclinic loopscontracting Lorenz attractors

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Bifurcations of singular points in dynamical systems (37G10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical aspects of attractors and their bifurcations (37G35) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (12)

Lorenz attractors in unfoldings of homoclinic-flip bifurcations ⋮ On the statistical stability of families of attracting sets and the contracting Lorenz attractor ⋮ The twisting bifurcations of double homoclinic loops with resonant eigenvalues ⋮ Contracting singular horseshoe ⋮ Multidimensional Rovella-like attractors ⋮ On the volume of singular-hyperbolic sets ⋮ Existence of periodic orbits and shift-invariant curve sequences near multiple homoclinics ⋮ Bifurcations of Double Homoclinic Loops in Reversible Systems ⋮ Decay of correlations, quantitative recurrence and logarithm law for contracting Lorenz attractors ⋮ Codimension 3 nontwisted double homoclinic loops bifurcations with resonant eigenvalues ⋮ Codimension 2 bifurcation of twisted double homoclinic loops ⋮ The Rovella attractor is asymptotically sectional-hyperbolic

This page was built for publication: Contracting Lorenz Attractors through Resonant Double Homoclinic Loops