4 papers · 1 filter
Forcing relations for homoclinic and periodic orbits of the Smale horseshoe map
Pieter Collins
An important problem in the dynamics of surface homeomorphisms is determining the forcing relation between orbits. The forcing relation between periodic orbits can be computed usin…
Entropy-minimising models of surface diffeomorphisms relative to homoclinic and heteroclinic orbits
Pieter Collins
In the theory of surface diffeomorphisms relative to homoclinic and heteroclinic orbits, it is possible to compute a one-dimensional representative map for any irreducible isotopy…
Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits
Pieter Collins
The Nielsen-Thurston theory of surface diffeomorphisms shows that useful dynamical information can be obtained about a surface diffeomorphism from a finite collection of periodic o…
Dynamics forced by surface trellises
Pieter Collins
Given a saddle fixed point of a surface diffeomorphism, its stable and unstable curves and often form a homoclinic tangle. Given such a tangle, we use topological metho…