Daily Dynamics & Continua Digest

Weekly summary · 2026-10-05 – 2026-10-09

Week 2026-W41

HIGH PRIORITY
10
RELATED / POSSIBLY INTERESTING
27
TOTAL PAPERS
172

Daily reports this week: , , , , . Low-priority papers are listed only in the daily reports.

High Priority

  1. DS · arXiv:2610.03327

    Open dynamical systems in topologically expansive decreasing Lorenz maps

    Yiming Ding, Wolfgang Steiner, Yun Sun

    The authors develop an admissibility theory for topologically expansive decreasing Lorenz maps and use it to study the negative doubling map with a hole. The Hausdorff dimension of the survivor set is a devil's staircase in the right endpoint of the hole.

    interval and graph mapssymbolic dynamicsfractals and dimension

  2. DS · arXiv:2610.03619

    Sturmian beta-shifts do not have typical periodic optimization

    Wen Huang, Oliver Jenkinson, Leiye Xu, Yiwei Zhang

    Beta-shifts whose lexicographically largest point is Sturmian do not have typical periodic optimization: an open set of Lipschitz functions is maximized only by the Sturmian measure. These are the first shifts with specification known to lack this property.

    symbolic dynamicsshadowing and specificationgenericity

  3. DS · arXiv:2610.04179

    Discontinuous Generalized Hyperbolicity and Structural Stability

    Sergey Tikhomirov

    A continuous-selection method gives semiconjugacies and structural stability for Banach-space dynamics with possibly discontinuous generalized-hyperbolic splittings. It also yields Lipschitz shadowing for an induced operator.

    shadowing and specificationsmooth and hyperbolic dynamics

  4. DS · arXiv:2610.05049

    Simultaneous renormalization of commuting circle diffeomorphisms

    Boris Petković

    A renormalization operator for pairs of commuting circle diffeomorphisms, driven by the Brun continued fraction algorithm, converges to rigid rotations. This gives simultaneous smooth conjugacy to rotations for a full-measure class of rotation vectors.

    circle and one-dimensional dynamicssmooth and hyperbolic dynamics

  5. DS · arXiv:2610.06418

    Unbounded orbits in C^1-generic centrally symmetric strictly convex outer billiards

    Alfonso Sorrentino

    For a residual set of centrally symmetric strictly convex C^1 tables, outer billiard maps have orbits escaping to infinity. This answers the Moser–Neumann question in that setting.

    planar and surface dynamicsgenericity

  6. DS · arXiv:2610.07435

    Period spectrum and rigidity of interval maps

    Gabriel Fuhrmann, Maik Gröger, Alejandro Passeggi

    Periodic orbits determine every topologically mixing interval map. For non-mixing maps with dense periodic points they determine the second iterate, and locally they determine an iterate on each basic set.

    interval and graph mapsmixing and transitivity

  7. DS · arXiv:2610.08426

    Shadowing and Topological Stability via Generalized Pseudo-Hyperbolicity in Autonomous and Nonautonomous Linear Dynamics

    Davor Dragicevic, Mihaly Pituk

    For sequences of invertible bounded linear operators on Banach spaces, generalized pseudo-hyperbolicity is equivalent to shadowing and to topological stability. In particular shadowing and topological stability coincide for single operators.

    shadowing and specification

  8. DS · arXiv:2608.30346

    Classification complexity of homeomorphism group actions

    Michal Hevessy, Benjamin Vejnar

    Replacing the full homeomorphism group of a compact metrizable space by natural dense non-closed subgroups can strictly increase, or make incomparable, the complexity of the associated orbit equivalence relations.

    hyperspaces and descriptive topologygroup actions

  9. DS · arXiv:2610.09482

    Typical expansive measures for infinite-dimensional maps

    Gabriel Lacerda

    The shift on the Hilbert cube is expansive with respect to product Lebesgue measure, so Mañé's finite-dimensionality theorem for expansive homeomorphisms does not extend to measure expansiveness.

    genericityshadowing and specification

  10. DS · arXiv:2610.11793

    Local Connectivity of the Filled Julia Set Bundle over the Mandelbrot Set

    Yueyang Wang

    The non-escaping locus of the quadratic family over the Mandelbrot set has boundary of full Hausdorff dimension 4 and is locally connected at hyperbolic parameters, but local connectedness fails at some real parabolic parameters.

    complex dynamicscontinuum theory

Related / Possibly Interesting

  1. DS · arXiv:2607.26572

    Near full groups of bounded type, II

    Zheng Kuang

    The author gives criteria for when a group of bounded type contains the AF alternating group of the tail groupoid, and shows that this containment is not determined by the groupoid of germs alone.

    group actionsminimal systems and factors

  2. DS · arXiv:2610.04745

    Entropic rates from eigenfunction structure for \times 2 \times 3

    Peter Burton, Kate Juschenko

    An effective Rudolph–Johnson bound is read as a constraint on eigenfunctions in potential counterexamples to Furstenberg's times-2 times-3 conjecture.

    ergodic theoryentropy and chaoscircle and one-dimensional dynamics

  3. DS · arXiv:2610.05626

    On global Lyapunov functions being Morse

    Wouter Jongeneel

    For a globally asymptotically stable hyperbolic equilibrium a Morse Lyapunov function exists, but not for every globally asymptotically stable equilibrium.

    flows and foliations

  4. DSGN · arXiv:2610.05805

    Temporal Metric Spaces and Temporal Iterated Function Systems

    Amal P. S., Vinod Kumar P. B., Ramkumar P. B

    The authors define interval-dependent metrics on trajectory spaces of evolving domains, study their topology and hyperspaces, and develop iterated function systems on them.

    hyperspaces and descriptive topologyfractals and dimension

  5. DS · arXiv:2610.06488

    On the centralizer and normalizer groups of odometers and Toeplitz subshifts

    Jaime Gómez, Samuel Petite

    For residually finite groups, the authors study automorphism and normalizer groups of odometers and Toeplitz subshifts, with an orbit-equivalence result for \mathbb Z^d and flexible examples for Toeplitz subshifts.

    symbolic dynamicsgroup actions

  6. DS · arXiv:2610.06713

    The Almost Finite–Purely Infinite Dichotomy for Minimal Amenable Ample Groupoids

    Gábor Elek, Ádám Timár

    A minimal principal topologically amenable ample groupoid with Cantor unit space is strongly almost finite exactly when it has an invariant probability measure, and purely infinite otherwise.

    group actionsminimal systems and factors

  7. DS · arXiv:2610.06586

    Classifiability of crossed products

    Eusebio Gardella

    A survey of crossed products of topological dynamical systems and their classifiability in the Elliott program, aimed both as an entry point and a reference.

    surveygroup actionsminimal systems and factors

  8. DS · arXiv:2205.01537

    Bratteli diagrams, translation flows and their C^*-algebras

    Ian F. Putnam, Rodrigo Treviño

    The authors connect the path space of a bi-infinite Bratteli diagram with the translation surface built from it, and relate the associated C*-algebras and their K-theory.

    symbolic dynamicsflows and foliations

  9. DS · arXiv:2610.07317

    Rudolph-Johnson without dynamics: endomorphic rigidity on the circle

    Peter Burton, Kate Juschenko

    Entropy alone, without invariance, pushes a measure on the circle toward Lebesgue measure under any sublacunary set of maps x\mapsto mx.

    ergodic theoryentropy and chaoscircle and one-dimensional dynamics

  10. DS · arXiv:2610.07347

    Mixing of the BCZ Map

    Albert Artiles, Andrew Best, Matteo Bordignon

    The Boca–Cobeli–Zaharescu map is strongly mixing with respect to normalized Lebesgue measure on the BCZ triangle.

    ergodic theorymixing and transitivity

  11. DS · arXiv:2610.08511

    Groupoid strict comparison for Ample Groupoids: Fiberwise Supramenability and Topological Amenability

    Chunlin Liu, Xin Ma, Jianchao Wu

    Fiberwise supramenability or topological amenability of a minimal ample groupoid gives an almost unperforated clopen type semigroup, hence groupoid strict comparison in the sigma-compact case.

    group actionsminimal systems and factors

  12. DS · arXiv:2610.08625

    An Entropy Bound for Mean Dimension of Open Covers

    Tal Barak

    The mean dimension of a finite open cover is bounded in terms of its topological entropy and cardinality, so mean dimension pairs are entropy pairs and uniformly positive mean dimension implies uniformly positive entropy.

    entropy and chaosgroup actions

  13. DS · arXiv:2610.09949

    Ergodic measures of intermediate entropies for amenable group actions with an approximate product property

    Wenda Zhang, Xiankun Ren

    An approximate product property for amenable group actions yields entropy-denseness, and with asymptotic entropy expansiveness every entropy in [0,h(X,G)) is realized by a residual set of ergodic measures.

    entropy and chaosgroup actionsshadowing and specification

  14. DS · arXiv:2610.09966

    Universal Dynamics in a family of Celestial Mechanics models

    Miguel Garrido, Pau Martín

    Every symplectic embedding of the disk into the plane is approximated by a renormalized Poincaré map of a suitable restricted planar circular many-body problem.

    celestial mechanics

  15. DS · arXiv:2610.09986

    Non-rigid disk pseudo-rotations in C^1 and C^{1,\beta}

    Ziran Liu, Jian Wang, Peizheng Yu

    The authors construct area-preserving irrational pseudo-rotations of the closed disk that are not C^0-rigid, arbitrarily close to the rigid rotation in C^1 or C^{1,\beta}.

    planar and surface dynamics

  16. DS · arXiv:2610.10101

    Variational Persistence of Periodic and Quasi-Periodic Orbits in Symmetric N-Body Problems

    Hangqi Liang, Zhihong Xia, Tingjie Zhou

    Rotational symmetry yields families of periodic and quasi-periodic N-body trajectories via variational persistence results.

    celestial mechanics

  17. DS · arXiv:2610.10397

    The regionally proximal relation for commutative semigroup actions

    Angelina Blahodatna, Lauren Detmold, Daniel Glasscock, Anh N. Le

    For minimal actions of commutative semigroups, the regionally proximal and equicontinuous structure relations are equivalence relations and coincide.

    minimal systems and factorsgroup actions

  18. DS · arXiv:2610.10416

    The local dynamical structure of \Delta^* sets via a new Furstenberg family algebra

    Angelina Blahodatna, Lauren Detmold, Daniel Glasscock, Anh N. Le

    Sets meeting every difference subset of a commutative semigroup have local Bohr structure.

    minimal systems and factors

  19. DS · arXiv:2608.12168

    Hyperbolicity and obstructions to PL actions of the circle

    Leonardo Dinamarca, Maximiliano Escayola, Sang-hyun Kim, Thomas Koberda

    Finitely generated groups of PL circle homeomorphisms satisfy a trichotomy, giving a free-or-surface alternative for word-hyperbolic such groups.

    group actionscircle and one-dimensional dynamics

  20. DS · arXiv:2610.10896

    The Milnor Fiber as a Local Conley Index

    Jean-Paul Brasselet, Nivaldo Grulha

    For a holomorphic germ with an isolated critical point, the origin is an isolated invariant set of the negative gradient flow of \operatorname{Re} f, with Conley index the suspension of the Milnor fibre.

    flows and foliations

  21. GN · arXiv:2610.11417

    A Universal Quasi-Polish Space

    Su Gao, Qingguo Li, Hualin Miao

    There is a universal quasi-Polish space containing every quasi-Polish space as a closed subspace, and in its hyperspace the Polish closed subspaces form a complete coanalytic set.

    hyperspaces and descriptive topology

  22. DS · arXiv:2610.11545

    Continuity of the Julia sets in non-archimedean and hybrid settings

    Alexandre Roy

    Analogues of the Mañé–Sad–Sullivan continuity of Julia sets in the Hausdorff topology hold for families of rational maps parametrized by Berkovich spaces and in the hybrid setting.

    complex dynamicshyperspaces and descriptive topology

  23. DS · arXiv:2610.11639

    Variational Principles for r-Neutralized Pfister-Sullivan Entropy

    Ercai Chen, Yunxiang Xie, Xiaoyao Zhou

    The authors disprove a variational conjecture of Dong and Qiao for r-neutralized entropy and establish variational formulas and bounds for r-neutralized Pfister–Sullivan entropy.

    entropy and chaos

  24. DS · arXiv:2610.12258

    Intersections of quantitative recurrence and badly approximable sets for expanding Markov maps

    Lingmin Liao, Na Yuan

    For expanding Markov interval maps, the Hausdorff dimension of recurrence sets intersected with dynamically badly approximable sets is given by the same pressure function as for the recurrence sets.

    interval and graph mapsfractals and dimension

  25. DS · arXiv:2610.10558

    Foliations forcing closed orbits

    Ellis Buckminster, Audrey Rosevear

    The authors characterize which finite depth foliations on atoroidal 3-manifolds force every transverse flow to have a closed orbit, and show this can often be broken by C^0-small changes.

    flows and foliations

  26. DS · arXiv:2610.12279

    Invariant sets and spectral rigidity of Hamiltonian diffeomorphisms

    Habib Alizadeh, Egor Shelukhin

    Every non-trivial Hamiltonian diffeomorphism of a surface of genus at least one has all positive iterates separated from the identity in Hofer's metric, answering a question of Polterovich.

    planar and surface dynamics

  27. DS · arXiv:2610.12302

    Drilling veering triangulations with applications to pseudo-Anosov flows

    Anna Parlak, Henry Segerman

    An algorithm drills closed orbits out of transitive pseudo-Anosov flows at the level of veering triangulations, giving computational evidence for a conjecture of Ghys.

    flows and foliationssmooth and hyperbolic dynamics

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