Discrete and Continuous Dynamical Systems - Series S: latest papers http://www.aimsciences.org/test_aims/journals/rss.jsp?journalID=15 Latest articles for selected journal http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13607 Spectral notions of aperiodic order http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13607 Michael Baake and Daniel Lenz Sat, 1 Apr 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13608 Stability of nonlinear waves: Pointwise estimates http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13608 Margaret Beck Sat, 1 Apr 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13609 A survey of complex dimensions, measurability, and the lattice/nonlattice dichotomy http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13609 complex dimensions of fractal strings developed by Lapidus and van Frankenhuijsen has proven to be a powerful tool for the study of Minkowski measurability of fractal subsets of the real line. In a very general setting, the Minkowski measurability of such sets is characterized by the structure of corresponding complex dimensions. Also, this tool is particularly effective in the setting of self-similar fractal subsets of $\mathbb{R}$ which have been shown to be Minkowski measurable if and only if they are nonlattice. This paper features a survey on the pertinent results of Lapidus and van Frankenhuijsen and a preliminary extension of the theory of complex dimensions to subsets of Euclidean space, with an emphasis on self-similar sets that satisfy various separation conditions. This extension is developed in the context of box-counting measurability, an analog of Minkowski measurability, which is shown to be characterized by complex dimensions under certain mild conditions. ]]> Kristin Dettmers, Robert Giza, Rafael Morales, John A. Rock and Christina Knox Sat, 1 Apr 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13610 Random interval diffeomorphisms http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13610 Masoumeh Gharaei and Ale Jan Homburg Sat, 1 Apr 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13611 Homoclinic tangencies to resonant saddles and discrete Lorenz attractors http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13611 Sergey Gonchenko and Ivan Ovsyannikov Sat, 1 Apr 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13612 A family of self-avoiding random walks interpolating the loop-erased random walk and a self-avoiding walk on the Sierpiński gasket http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13612 Kumiko Hattori, Noriaki Ogo and Takafumi Otsuka Sat, 1 Apr 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13613 Stability index, uncertainty exponent, and thermodynamic formalism for intermingled basins of chaotic attractors http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13613 Gerhard Keller Sat, 1 Apr 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13614 A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13614 Marc Kesseböhmer and Sabrina Kombrink Sat, 1 Apr 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13615 Derivatives of slippery Devil's staircases http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13615 Jun-Jie Miao and Sara Munday Sat, 1 Apr 2017 20:00:00 GMT http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13616 Variational principles for the topological pressure of measurable potentials http://www.aimsciences.org/test_aims/journals/displayPaper.jsp?paperID=13616 Marc Rauch Sat, 1 Apr 2017 20:00:00 GMT