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We formulate a strengthening of the Zariski dense orbit conjecture for birational maps of dynamical degree one. So, given a quasiprojective variety $X$ defined over an algebraically closed field $K$ of characteristic $0$, endowed with a…
Let $f:X\to X$ be a non-isomorphic (i.e., $\text{deg } f>1$) surjective endomorphism of a smooth projective threefold $X$. We prove that any birational minimal model program becomes $f$-equivariant after iteration, provided that $f$ is…
We prove that for any two continuous minimal (topologically free) actions of the infinite dihedral group on an infinite compact Hausdorff space, they are continuously orbit equivalent only if they are conjugate. We also show the above fails…
Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is…
Orbit separation dimension (OSD), previously introduced as amorphic complexity, is a powerful complexity measure for topological dynamical systems with pure-point spectrum. Here, we develop methods and tools for it that allow a systematic…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
In recent papers by the authors (S.~Motonaga and K.~Yagasaki, Obstructions to integrability of nearly integrable dynamical systems near regular level sets, submitted for publication, and K.~Yagasaki, Nonintegrability of nearly integrable…
We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…
We introduce and study dynamical systems and measures on stationary generalized Bratteli diagrams $B$ that are represented as the union of countably many classical Pascal-Bratteli diagrams. We describe all ergodic tail invariant measures on…
In this work we revisit the proposed multi-circumbinary system RZ Dra. We find the proposed system to be highly unstable. We attempt to find a best-fit light-travel time model rendering the orbits to follow stable orbits. We found a…
This paper will discuss the problem of defining the new topological transitivity. To do this several equivalent topological transitive and non-wandering point has been discussed through this paper. This paper also consider the ideal version…
We discuss analytical approximation schemes for the dynamics of diluted spin models. The original dynamics of the complete set of degrees of freedom is replaced by a hierarchy of equations including an increasing number of global…
A semi-relativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach…
We show that within any strong orbit equivalent class, there exist minimal subshifts with arbitrarily low superlinear complexity. This is done by proving that for any simple dimension group with unit $(G,G^+,u)$ and any sequence of positive…
Let $\Sigma$ and $\bar\Sigma$ be finite alphabets. For topologically transitive sofic systems $ X\subset \Sigma^{\Bbb Z}$ and $\widetilde X\subset \widetilde\Sigma^{\Bbb Z}$ we give a necessary and sufficient condition for the existence of…
Using a group-theoretic approach, a method for determining the equivalence classes (also called orbits) of the set of rules of one-dimensional cellular automata induced by the symmetry operations of reflection and permutation and their…
The phase space of a Hamiltonian system is symplectic. However, the post-Newtonian Hamiltonian formulation of spinning compact binaries in existing publications does not have this property, when position, momentum and spin variables $[X, P,…
It is very well known that periodic orbits of autonomous Hamiltonian systems are generically organized into smooth one-parameter families (the parameter being just the energy value). We present a simple example of an integrable Hamiltonian…
{\abstract{\textwidth=4,5 in} A discrete time process, with law $\mu$, is quasi-exchangeable if for any finite permutation $\sigma$ of time indices, the law $\mu_\sigma$ of the resulting process is equivalent to $\mu$. For a…
Let a compact torus $T=T^{n-1}$ act on an orientable smooth compact manifold $X=X^{2n}$ effectively, with nonempty finite set of fixed points, and suppose that stabilizers of all points are connected. If $H^{odd}(X)=0$ and the weights of…