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Inverse problems of symbolic dynamics

Alexei Ya. Belov, Grigorii V. Kondakov, Ivan V. Mitrofanov (2011)

Banach Center Publications

This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval exchange transformation. Rauzy graphs language can express many important combinatorial and some dynamical properties. In this case combinatorial properties are considered as being generated by a substitutional system, and dynamical properties are considered...

Investigation of the Migration/Proliferation Dichotomy and its Impact on Avascular Glioma Invasion

K. Böttger, H. Hatzikirou, A. Chauviere, A. Deutsch (2012)

Mathematical Modelling of Natural Phenomena

Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous cell proliferation and motility rates. The interplay of proliferation and migration dynamics plays an important role in the invasion of these malignant tumors. We analyze the regulation of proliferation and migration processes with a lattice-gas cellular automaton (LGCA). We study and characterize the influence of the migration/proliferation dichotomy (also known...

Irrational life.

Geller, William, Misiurewicz, Michał (2005)

Experimental Mathematics

Irreducible complexity of iterated symmetric bimodal maps.

Lampreia, J.P., Severino, R., Sousa Ramos, J. (2005)

Discrete Dynamics in Nature and Society

Iteration of a quaternionic quadratic family.

Skapin-Rugelj, Meta (1996)

Aequationes mathematicae

Iterations of rational functions: which hyperbolic components contain polynomials?

Feliks Przytycki (1996)

Fundamenta Mathematicae

Let $H^{d}$ be the set of all rational maps of degree d ≥ 2 on the Riemann sphere, expanding on their Julia set. We prove that if $f \in H^{d}$ and all, or all but one, critical points (or values) are in the basin of immediate attraction to an attracting fixed point then there exists a polynomial in the component H(f) of $H^{d}$ containing f. If all critical points are in the basin of immediate attraction to an attracting fixed point or a parabolic fixed point then f restricted to the Julia set is conjugate to the shift...