Saddle-focus singular cycles and prevalence of hyperbolicity
Shift spaces and attractors in noninvertible horseshoes
As is well known, a horseshoe map, i.e. a special injective reimbedding of the unit square in (or more generally, of the cube in ) as considered first by S. Smale [5], defines a shift dynamics on the maximal invariant subset of (or ). It is shown that this remains true almost surely for noninjective maps provided the contraction rate of the mapping in the stable direction is sufficiently strong, and bounds for this rate are given.
Sinai-Bowen-Ruelle measures for certain Hénon maps.
Smooth transformations of intervals
Smoothness of the attractor of almost all solutions of a delay differential equation [Book]
Some continuity and approximation properties of a countable iterated function system.
Some remarks on recent results about S-unimodal maps
Stable global attractors in
Strong cellularity and global asymptotic stability
Structural stability of Lorenz attractors
Study of the Iterations of a Mapping Associated to a Spin Glass Model
Subadditive Pressure for IFS with Triangular Maps
We investigate properties of the zero of the subadditive pressure which is a most important tool to estimate the Hausdorff dimension of the attractor of a non-conformal iterated function system (IFS). Our result is a generalization of the main results of Miao and Falconer [Fractals 15 (2007)] and Manning and Simon [Nonlinearity 20 (2007)].
Subcontinua of inverse limit spaces of unimodal maps
We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal maps as...
Synchronization of nonautonomous dynamical systems.