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pro vyhledávání: '"Leo, Roberto"'
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. We define two
Externí odkaz:
http://arxiv.org/abs/2410.05520
Autor:
De Leo, Roberto, Yorke, James A.
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 it to Axiom-A diffeomorphisms on manifolds. In Smale's vision, nodes a
Externí odkaz:
http://arxiv.org/abs/2401.12327
Autor:
Anusic, Ana, De Leo, Roberto
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, jointly with J. Yorke, studied the graph and backward limits of S-uni
Externí odkaz:
http://arxiv.org/abs/2302.04342
Autor:
De Leo, Roberto
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 points of all backward trajectories through $x$ was called by M.~Hero t
Externí odkaz:
http://arxiv.org/abs/2109.02759
Autor:
De Leo, Roberto, Yorke, James A.
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The qualitative behav
Externí odkaz:
http://arxiv.org/abs/2101.00306
Autor:
De Leo, Roberto, Yorke, James A.
The qualitative behavior of a dynamical system can be encoded in a graph. Each node of the graph is an equivalence class of chain-recurrent points and there is an edge from node $A$ to node $B$ if, using arbitrary small perturbations, a trajectory st
Externí odkaz:
http://arxiv.org/abs/2008.08338
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Autor:
Ghilardi, Alessandra, Frate, Guido Francesco, Tucci, Mauro, Bravi, Mirko, Leo, Roberto, Ferrari, Lorenzo
Publikováno v:
In Journal of Energy Storage 15 October 2023 70
Autor:
De Leo, Roberto
We study numerically the $\alpha$- and $\omega$-limits of the Newton maps of two of the most elementary families of polynomial transformations on the plane: those with a linear component and those with both components of degree two. Our results are f
Externí odkaz:
http://arxiv.org/abs/1812.11595
Autor:
De Leo, Roberto
We collect from several sources some of the most important results on the forward and backward limits of points under real and complex rational functions, and in particular real and complex Newton maps, and we provide numerical evidence that a fundam
Externí odkaz:
http://arxiv.org/abs/1812.00270