8 research outputs found
Statistical properties of mostly contracting fast-slow partially hyperbolic systems
No full textWe consider a class of C
4 partially hyperbolic systems on T
2 described
by maps Fε(x, θ) = (f(x, θ), θ + εω(x, θ)) where f(·, θ) are expanding
maps of the circle. For sufficiently small ε and ω generic in an open set, we
precisely classify the SRB measures for Fε and their statistical properties, including
exponential decay of correlation for H¨older observables with explicit
and nearly optimal bounds on the decay rate
Potts models on hierarchical lattices and renormalization group dynamics
No full textWe prove that the generator of the renormalization group of Potts models on hierarchical lattices can be represented by a rational map acting on a finite-dimensional product of complex projective spaces. In this framework, we can also consider models with an applied external magnetic field and multiple-spin interactions. We use recent results regarding iteration of rational maps in several complex variables to show that, for some class of hierarchical lattices, Lee–Yang and Fisher zeros belong to the unstable set of the renormalization map
The Martingale approach after Varadhan and Dolpogpyat
No full textWe present, in the simplest possible form, the so called {\em martingale problem} strategy to establish limit
theorems. The presentation is specially adapted to problems arising in partially hyperbolic dynamical systems. We will
discuss a simple partially hyperbolic example with fast-slow variables and use the martingale method to prove an
averaging theorem and study fluctuations from the average. The emphasis is on ideas rather than on results. Also, no
effort whatsoever is done to review the vast literature of the field
A Three Invariant Formulation for Steel Behavior: Experimental Observations and Constitutive Models
No full textCan you hear the shape of a drum and deformational spectral rigidity of planar domains?
No full textM. Kac popularized the question {\em Can you hear the shape of a drum?}
Mathematically, consider a bounded planar domain and the associated
Dirichlet problem with = 0. The set of
s such that this equation has a solution, denoted
is called the Laplace spectrum of
Does Laplace spectrum determine ? In general, the answer is negative.
Consider the billiard problem inside ?. Call the length spectrum the
closure of the set of perimeters of all periodic orbits of the billiard. Due
to deep properties of the wave trace function, generically, the Laplace
spectrum determines the length spectrum. We show that any generic axis
symmetric planar domain with is dynamically spectrally rigid, i.e. can't be
deformed without changing the length spectrum. This partially answers a
question of P. Sarnak. This is joint works with J. De Simoi, A. Figalli, and
J. De Simoi, Q. Wei.Non UBCUnreviewedAuthor affiliation: University of MarylandFacult
Actinopus simoi Duniesky 2019, sp. nov.
No full textActinopus simoi sp. nov. (Figs 6, 7, 10) urn:lsid:zoobank.org:act: 9ECF08C7-59B6-4B09-8769-B9CAFA1F0042 Type material: Uruguay: Maldonado. Holotype ♂: Cerro San Antonio [34°52′S 55°16′W], 15 February 1980, M. Estoll (MNHN 1310) . Paratype ♀: San Carlos [34°48′S 54°55′W], 9 January 1978, R. Capocasale (MNHN 1281). Other material examined. Uruguay: Maldonado: Sierra de Animas [34°45′S 55°19′W], E. García & J. Ro- dríguez, 10 January 1971, 1♀ (MNHN 632) ; Canelones: Balneario Solis [34°47′S 55°23′W], A. Leep, 1 December 1974, 1♂ (MNHN 666). Etymology. The specific name is a patronym in honor of Dr. Miguel Simó Núñez, for his contributions to the knowledge of Uruguayan spiders. Diagnosis. Males of A. simoi differ from those of all other species by the dark body colour; they resemble those of A. liodon but differ in leg coloration, with red metatarsi-tarsi and palp tibiae (Fig. 6E); they can by recognized by a chelicerae prolongation without cuspules (like A. liodon and A. longipalpis). Males also differ from those of A. longipalpis by their copulatory bulb shape (Fig. 6 F–H). Females can be distinguished from those of other species by the shape of their spermathecae (Fig. 7F, G) with a small external lobe, similar to that of A. insignis but differ by their booklung with dark markings and a longer sternum. Description. (Fig. 6). Male holotype (MNHN 1310). Total length: 12.20. Carapace (Fig. 6A): length 5.80, width 5.50; cephalic region: length 3.40, width 4.20; clypeus small, 11 bristles between PME, 4 behind each PME- PLE, 4 bristles and one larger on both sides of ocular group. Fovea: length 1.00, width 2.50. Eyes, diameters and interdistances: AME 0.26 (large), ALE 0.32, PME 0.16, PLE 0.32, ocular group length 0.90, anterior width 2.60, 2.38 posterior width; AME-ALE 0.69, PME-PLE 0.16, AME-PME 0.37, ALE-PLE 0.42, AME-AME 0.21. Chelicerae: length 2.60, width 1.30; cheliceral apex with 12 recumbent and elongated bristles which cover fang base. Cheliceral prolongation without cuspules. Cheliceral furrow (Fig. 6C) with 6 large promarginal and 5 retromarginal teeth (small one between 3th–4th and 4th–5th) and 10 denticles, near promarginal teeth. Labium: length 0.90, width 1.10. Maxillae: anterior length 1.50, posterior length 2.20, width 1.40. Sternum: Center flat (Fig. 6B): length 4.00, maximum width 3.20, minimum width 1.10. Postlabial sigilla shallow, posterior sigilla well defined. Abdomen (very compressed due to poor preservation): length ~ 5.40, large, covered by bristles. Spinnerets compressed. Lengths of legs and palp: I: 5.50, 2.20, 3.10, 3.80, 2.20, 16.80. II: 5.50, 2.20, 3.10, 3.80, 2.00, 16.60. III: 4.20, 2.20, 2.50, 4.50, 2.00, 15.40. IV: 5.50, 2.50, 4.50, 4.50, 2.50, 19.50. Palp: 5.50, 2.60, 4.20,–, 1.40, 13.70. Chaetotaxy: Femora: I–IV, 0. Patellae: I–II: 0; III, 35 P SUP-D ANT + 10 on margin, 1-1-1-1 D (2:3 B), 7 R A + 11 on margin; IV, 54 P SUP- D ANT. Tibia: I, 1-1- 3 V (1:2 A); II, 1-2-2-3-4-2-3 R, 1-2-1- 3 V; III, 1 P, 1 D (1:2 B), 1-1 R (1:3 A), 1- 4 V A, with apical crown of 19 thorns; IV, 1-1-2 P, 1-1-2- 3 V. Metatarsi: I, 1-0-1- 1 V ANT, 2-2-1-1- 2 V POST; II, 1-1- 2 V ANT, 2-1-2-1-2-2-1- 4 V POST; III, 1-3-1-2-1-1-3 P, 1 D A, 2-2-2-1-1-3-3-4 D POST-R SUP, 2-3-3-1-1-1-2- 2 V; IV, 1-2-2- 2-2-1-3 P, 2-1-1-1- 4 V. Tarsi: I, 1-1-1-1 P INF, 16 R INF; II, 2-1-1-1-2-2-1 P INF, 19 R INF; III, 12 P INF, 18 R INF; IV, 20 P INF, 13 R A. Total number of retrolateral spines on tibiae I, II (Fig. 6D): 0 and 17, respectively. Palp: tibiae short, thickened (Fig. 6E). Bulb (Fig. 6 F–H) with ATA and BTA developed, embolus with series of denticles at base. Scopulae: Tarsi: I–II, sparse 1:2 apical; III–IV, dense, uniform. Metatarsi: IV sparse 1:4 A. Trichobothria: Tibiae: I–II 4-3; III 5-4; IV 6-5. Metatarsi: I–II 10; III 8; IV 7. Tarsi: I 9; II 7; III 9; IV 7. Color: carapace and chelicerae black. Abdomen dark brown; booklungs with dark markings. Sternum, labium and maxillae dark reddish brown. Legs like carapace with lighter tarsi-metatarsi; palp with lighter tibiae. Female paratype (MNHN 1281). Total length: 16.20. Carapace (Fig. 7A): length 6.40, width 6.30; with 12 bristles on each posterior margin; cephalic region: length 3.70, width 5.30; clypeus small with 18 bristles, 9 on chillum; 12 bristles between PME and 4 behind each PME-PLE, 6 bristles and one larger on both sides of ocular group. Fovea: length 1.20, width 3.00. Eyes, diameters and interdistances: AME 0.21, ALE 0.42, PME 0.21, PLE 0.26, ocular group 1.06, anterior width 3.55, 3.34 posterior width; AME-ALE 1.06, PME-PLE 0.21, AME-PME 0.72, ALE-PLE 0.58, AME-AME 0.32. Chelicerae: Length 2.80, width 2.10, chelicerae apex with 12 recumbent and elongated bristles covering fang base. Rastellum with 11 marginal, blunt spines and 7 small dorsal. Cheliceral furrow (Fig. 7C) with 5 promarginal and 4 retromarginal teeth, and 10 denticles in furrow, near promargin. Labium: length 1.10, width 1.30, with 10 anterior cuspules. Maxillae: anterior length 2.10, posterior length 2.50, width 1.40, with 60 cuspules 1: 3 V ANT, expanding to anterior face. Sternum: Center flat (Fig, 7B), length: 5.30, maximum wide 4.20, minimum width 1.30. Postlabial sigilla deep, posterior sigilla shallow, well defined. Abdomen: length 11.00, covered by dark bristles. PMS: length 0.79; PLS with basal: medial: apical articles 0.79:0.42:0.26. Spigots: 2 large, 25 small on PMS; PLS, numbers of large (small) spigots on basal: medial: apical article 3(35):2(+20):0(~50). Lengths of legs and palp: I: 3.40, 2.40, 1.60, 2.20, 1.10, 10.70. II: 3.40, 2.50, 1.60, 2.30, 1.10, 10.90. III: 3.00, 2.70, 1.20, 2.50, 1.00, 10.40. IV: 4.00, 2.80, 2.50, 2.70, 0.80, 12.80. Palp: 3.20, 2.20, 2.20,–, 2.50, 10.10. Chaetotaxy: All femora: 0. Patellae: I–II, 0; III, 20 P A + 13 on the margin, 25 R A + 14 on the margin; IV, 71 P SUP-D ANT; palp, 1-1- 1 p. Tibiae: I, 5-11 R, 1/1- 1 V POST; II, 85 R; III, 1 D B, with apical crown of 19 thorns and 6 apical (at apex, anterior to crown), 50 R; IV, 0; palp, 1-1-1 P INF, 1-1-1 p, 17 R INF. Metatarsi: I, 18 P INF, 1-1- 1 V POST, 24 R INF; II, 7 P INF, 12 R INF, 1-1- 2 V POST; III, 28 D ANT-P SUP, 50 on row D POST-R (more abundant R A); IV, 12 P INF, 1 D A. Tarsi: I, 9 P INF, 13 R INF, 1 V A; II, 12 P INF, 9 R INF, 1 V A; III, 22 R, 87 V-P; IV, 82 V-P; palp, 17 P INF, 28 R INF, 2 V A. Total number of retrolateral spines on tibiae I, II (Fig. 7D): 16 and 85, respectively. Trichobothria: Tibiae: I 4-5; II–III 6-4; IV 7-6. Metatarsi: I 11; II 10; III 9; IV 5. Tarsi: I 7; II 9; III 11; IV 5. Color: carapace, cephalic region, legs and chelicerae dark reddish brown. Abdomen brown; booklungs with dark markings (Fig. 7D). Sternum light reddish brown, darker labium and maxillae. Spinnerets dark. Distribution. Currently known only from Maldonado province, but may be more widespread in southern Uruguay (Fig.10).Published as part of Duniesky, Rios-Tamayo, 2019, Four new species of Actinopus (Mygalomorphae: Actinopodidae) from Uruguay, pp. 523-538 in Zootaxa 4624 (4) on pages 530-533, DOI: 10.11646/zootaxa.4624.4.5, http://zenodo.org/record/326558
Fast–Slow Partially Hyperbolic Systems Versus Freidlin–Wentzell Random Systems
No full textWe consider a simple class of fast-slow partially hyperbolic dynamical
systems and show that the (properly rescaled) behaviour of the slow
variable is very close to a Friedlin–Wentzell type random system for times that
are rather long, but much shorter than the metastability scale. Also, we show
the possibility of a “sink” with all the Lyapunov exponents positive, a phenomenon
that turns out to be related to the lack of absolutely continuity of
the central foliation
