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The Chain Graph of a general Iterated Function System
Roberto De Leo
Classical fractal geometry describes the metric and topological structure of attractors generated by contractive Iterated Function Systems (IFSs). Much less is known about their gl…
Recurrent and gradient dynamics of Iterated Function Systems
Roberto De Leo
We study the qualitative dynamics of general Iterated Function Systems (IFSs) through chain recurrence and a decomposition into recurrent and gradient-like behavior. At the same ti…
Shadow chains and Conley chains for continuous-time semiflows
Roberto De Leo, James A. Yorke
In a recent series of articles we introduced the concept of "stream of a semiflow. A stream is a closed and transitive binary relation which extends the relation "being on the orbi…
Streams and Graphs of Dynamical Systems
Roberto De Leo, James A. Yorke
While studying gradient dynamical systems (DSs), Morse introduced the idea of encoding the qualitative behavior of a DS into a graph. Smale later refined Morse's idea and extended…
Graph and backward asymptotics of the tent map
Ana Anusic, Roberto De Leo
The tent map family is arguably the simplest 1-parametric family of maps with non-trivial dynamics and it is still an active subject of research. In recent works the second author,…
Backward asymptotics in S-unimodal maps
Roberto De Leo
While the forward trajectory of a point in a discrete dynamical system is always unique, in general a point can have infinitely many backward trajectories. The union of the limit p…
Exponential growth of norms in semigroups of linear automorphisms and Hausdorff dimension of self-projective IFS
Roberto De Leo
Given a finitely generated semigroup S of the (normed) set of linear maps of a vector space V into itself, we find sufficient conditions for the exponential growth of the number N(…